# Real-Valued Function Graph Foundations

This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.

This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.

batch-20261003-r06-function-graph-foundations · 2026-10-03 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.



## 1. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={-12, -11, -10} and f:D→R is given by f(x)=(-2)x+(-1). Does (-9, 17) belong to the declared graph?

View answer and explanationNo

The input -9 does not belong to D, and the formula value is 17. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0001/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 2. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={-11, -10, -9} and f:D→R is given by f(x)=(-1)x+(0). Does (-10, 11) belong to the declared graph?

View answer and explanationNo

The input -10 belongs to D, and the formula value is 10. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0002/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 3. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={-10, -9, -8} and f:D→R is given by f(x)=(0)x+(1). Does (-8, 1) belong to the declared graph?

View answer and explanationYes

The input -8 belongs to D, and the formula value is 1. Both the domain and output conditions must hold, giving Yes. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0003/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 4. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={-9, -8, -7} and f:D→R is given by f(x)=(1)x+(2). Does (-6, -4) belong to the declared graph?

View answer and explanationNo

The input -6 does not belong to D, and the formula value is -4. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0004/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 5. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={-8, -7, -6} and f:D→R is given by f(x)=(2)x+(-1). Does (-7, -14) belong to the declared graph?

View answer and explanationNo

The input -7 belongs to D, and the formula value is -15. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0005/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 6. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={-7, -6, -5} and f:D→R is given by f(x)=(-2)x+(0). Does (-5, 10) belong to the declared graph?

View answer and explanationYes

The input -5 belongs to D, and the formula value is 10. Both the domain and output conditions must hold, giving Yes. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0006/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 7. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={-6, -5, -4} and f:D→R is given by f(x)=(-1)x+(1). Does (-3, 4) belong to the declared graph?

View answer and explanationNo

The input -3 does not belong to D, and the formula value is 4. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0007/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 8. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={-5, -4, -3} and f:D→R is given by f(x)=(0)x+(2). Does (-4, 3) belong to the declared graph?

View answer and explanationNo

The input -4 belongs to D, and the formula value is 2. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0008/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 9. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={-4, -3, -2} and f:D→R is given by f(x)=(1)x+(-1). Does (-2, -3) belong to the declared graph?

View answer and explanationYes

The input -2 belongs to D, and the formula value is -3. Both the domain and output conditions must hold, giving Yes. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0009/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 10. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={-3, -2, -1} and f:D→R is given by f(x)=(2)x+(0). Does (0, 0) belong to the declared graph?

View answer and explanationNo

The input 0 does not belong to D, and the formula value is 0. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0010/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 11. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={-2, -1, 0} and f:D→R is given by f(x)=(-2)x+(1). Does (-1, 4) belong to the declared graph?

View answer and explanationNo

The input -1 belongs to D, and the formula value is 3. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0011/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 12. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={-1, 0, 1} and f:D→R is given by f(x)=(-1)x+(2). Does (1, 1) belong to the declared graph?

View answer and explanationYes

The input 1 belongs to D, and the formula value is 1. Both the domain and output conditions must hold, giving Yes. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0012/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 13. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={0, 1, 2} and f:D→R is given by f(x)=(0)x+(-1). Does (3, -1) belong to the declared graph?

View answer and explanationNo

The input 3 does not belong to D, and the formula value is -1. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0013/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 14. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={1, 2, 3} and f:D→R is given by f(x)=(1)x+(0). Does (2, 3) belong to the declared graph?

View answer and explanationNo

The input 2 belongs to D, and the formula value is 2. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0014/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 15. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={2, 3, 4} and f:D→R is given by f(x)=(2)x+(1). Does (4, 9) belong to the declared graph?

View answer and explanationYes

The input 4 belongs to D, and the formula value is 9. Both the domain and output conditions must hold, giving Yes. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0015/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 16. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={3, 4, 5} and f:D→R is given by f(x)=(-2)x+(2). Does (6, -10) belong to the declared graph?

View answer and explanationNo

The input 6 does not belong to D, and the formula value is -10. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0016/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 17. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={4, 5, 6} and f:D→R is given by f(x)=(-1)x+(-1). Does (5, -5) belong to the declared graph?

View answer and explanationNo

The input 5 belongs to D, and the formula value is -6. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0017/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 18. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={5, 6, 7} and f:D→R is given by f(x)=(0)x+(0). Does (7, 0) belong to the declared graph?

View answer and explanationYes

The input 7 belongs to D, and the formula value is 0. Both the domain and output conditions must hold, giving Yes. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0018/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 19. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={6, 7, 8} and f:D→R is given by f(x)=(1)x+(1). Does (9, 10) belong to the declared graph?

View answer and explanationNo

The input 9 does not belong to D, and the formula value is 10. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0019/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 20. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={7, 8, 9} and f:D→R is given by f(x)=(2)x+(2). Does (8, 19) belong to the declared graph?

View answer and explanationNo

The input 8 belongs to D, and the formula value is 18. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0020/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 21. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={8, 9, 10} and f:D→R is given by f(x)=(-2)x+(-1). Does (10, -21) belong to the declared graph?

View answer and explanationYes

The input 10 belongs to D, and the formula value is -21. Both the domain and output conditions must hold, giving Yes. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0021/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 22. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={9, 10, 11} and f:D→R is given by f(x)=(-1)x+(0). Does (12, -12) belong to the declared graph?

View answer and explanationNo

The input 12 does not belong to D, and the formula value is -12. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0022/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 23. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={10, 11, 12} and f:D→R is given by f(x)=(0)x+(1). Does (11, 2) belong to the declared graph?

View answer and explanationNo

The input 11 belongs to D, and the formula value is 1. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0023/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 24. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={11, 12, 13} and f:D→R is given by f(x)=(1)x+(2). Does (13, 15) belong to the declared graph?

View answer and explanationYes

The input 13 belongs to D, and the formula value is 15. Both the domain and output conditions must hold, giving Yes. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0024/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 25. Graph Membership with a Domain Restriction

In a fixed Cartesian coordinate system, D={12, 13, 14} and f:D→R is given by f(x)=(2)x+(-1). Does (15, 29) belong to the declared graph?

View answer and explanationNo

The input 15 does not belong to D, and the formula value is 29. Both the domain and output conditions must hold, giving No. An algebraic value outside D is not a value of the declared function there.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0025/)

Graphs of real-valued functions · qf-function-graph-membership · candidate





## 26. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={-12, -11, -10} and f:D→R is given by f(x)=(-2)x+(-1). Which ordered graph point corresponds to the permitted input -12?

View answer and explanation(-12, 23)

The point is (-12, 23). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0026/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 27. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={-11, -10, -9} and f:D→R is given by f(x)=(-1)x+(0). Which ordered graph point corresponds to the permitted input -10?

View answer and explanation(-10, 10)

The point is (-10, 10). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0027/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 28. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={-10, -9, -8} and f:D→R is given by f(x)=(0)x+(1). Which ordered graph point corresponds to the permitted input -8?

View answer and explanation(-8, 1)

The point is (-8, 1). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0028/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 29. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={-9, -8, -7} and f:D→R is given by f(x)=(1)x+(2). Which ordered graph point corresponds to the permitted input -9?

View answer and explanation(-9, -7)

The point is (-9, -7). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0029/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 30. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={-8, -7, -6} and f:D→R is given by f(x)=(2)x+(-1). Which ordered graph point corresponds to the permitted input -7?

View answer and explanation(-7, -15)

The point is (-7, -15). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0030/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 31. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={-7, -6, -5} and f:D→R is given by f(x)=(-2)x+(0). Which ordered graph point corresponds to the permitted input -5?

View answer and explanation(-5, 10)

The point is (-5, 10). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0031/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 32. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={-6, -5, -4} and f:D→R is given by f(x)=(-1)x+(1). Which ordered graph point corresponds to the permitted input -6?

View answer and explanation(-6, 7)

The point is (-6, 7). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0032/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 33. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={-5, -4, -3} and f:D→R is given by f(x)=(0)x+(2). Which ordered graph point corresponds to the permitted input -4?

View answer and explanation(-4, 2)

The point is (-4, 2). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0033/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 34. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={-4, -3, -2} and f:D→R is given by f(x)=(1)x+(-1). Which ordered graph point corresponds to the permitted input -2?

View answer and explanation(-2, -3)

The point is (-2, -3). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0034/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 35. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={-3, -2, -1} and f:D→R is given by f(x)=(2)x+(0). Which ordered graph point corresponds to the permitted input -3?

View answer and explanation(-3, -6)

The point is (-3, -6). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0035/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 36. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={-2, -1, 0} and f:D→R is given by f(x)=(-2)x+(1). Which ordered graph point corresponds to the permitted input -1?

View answer and explanation(-1, 3)

The point is (-1, 3). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0036/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 37. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={-1, 0, 1} and f:D→R is given by f(x)=(-1)x+(2). Which ordered graph point corresponds to the permitted input 1?

View answer and explanation(1, 1)

The point is (1, 1). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0037/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 38. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={0, 1, 2} and f:D→R is given by f(x)=(0)x+(-1). Which ordered graph point corresponds to the permitted input 0?

View answer and explanation(0, -1)

The point is (0, -1). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0038/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 39. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={1, 2, 3} and f:D→R is given by f(x)=(1)x+(0). Which ordered graph point corresponds to the permitted input 2?

View answer and explanation(2, 2)

The point is (2, 2). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0039/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 40. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={2, 3, 4} and f:D→R is given by f(x)=(2)x+(1). Which ordered graph point corresponds to the permitted input 4?

View answer and explanation(4, 9)

The point is (4, 9). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0040/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 41. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={3, 4, 5} and f:D→R is given by f(x)=(-2)x+(2). Which ordered graph point corresponds to the permitted input 3?

View answer and explanation(3, -4)

The point is (3, -4). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0041/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 42. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={4, 5, 6} and f:D→R is given by f(x)=(-1)x+(-1). Which ordered graph point corresponds to the permitted input 5?

View answer and explanation(5, -6)

The point is (5, -6). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0042/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 43. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={5, 6, 7} and f:D→R is given by f(x)=(0)x+(0). Which ordered graph point corresponds to the permitted input 7?

View answer and explanation(7, 0)

The point is (7, 0). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0043/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 44. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={6, 7, 8} and f:D→R is given by f(x)=(1)x+(1). Which ordered graph point corresponds to the permitted input 6?

View answer and explanation(6, 7)

The point is (6, 7). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0044/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 45. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={7, 8, 9} and f:D→R is given by f(x)=(2)x+(2). Which ordered graph point corresponds to the permitted input 8?

View answer and explanation(8, 18)

The point is (8, 18). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0045/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 46. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={8, 9, 10} and f:D→R is given by f(x)=(-2)x+(-1). Which ordered graph point corresponds to the permitted input 10?

View answer and explanation(10, -21)

The point is (10, -21). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0046/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 47. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={9, 10, 11} and f:D→R is given by f(x)=(-1)x+(0). Which ordered graph point corresponds to the permitted input 9?

View answer and explanation(9, -9)

The point is (9, -9). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0047/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 48. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={10, 11, 12} and f:D→R is given by f(x)=(0)x+(1). Which ordered graph point corresponds to the permitted input 11?

View answer and explanation(11, 1)

The point is (11, 1). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0048/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 49. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={11, 12, 13} and f:D→R is given by f(x)=(1)x+(2). Which ordered graph point corresponds to the permitted input 13?

View answer and explanation(13, 15)

The point is (13, 15). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0049/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 50. Graph Point for a Permitted Input

In a fixed Cartesian coordinate system, D={12, 13, 14} and f:D→R is given by f(x)=(2)x+(-1). Which ordered graph point corresponds to the permitted input 12?

View answer and explanation(12, 23)

The point is (12, 23). Its first coordinate is the permitted input in D and its second coordinate is the unique output.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0050/)

Graphs of real-valued functions · qf-function-graph-point · candidate





## 51. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D=∅ and f:D→R is given by f(x)=(-2)x+(-1). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation∅

For every input in D, list (x,f(x)). The graph is ∅; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0051/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 52. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={0} and f:D→R is given by f(x)=(-1)x+(0). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(0, 0)}

For every input in D, list (x,f(x)). The graph is {(0, 0)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0052/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 53. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={-10, -9, -8} and f:D→R is given by f(x)=(0)x+(1). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(-10, 1), (-9, 1), (-8, 1)}

For every input in D, list (x,f(x)). The graph is {(-10, 1), (-9, 1), (-8, 1)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0053/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 54. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={-9, -8, -7} and f:D→R is given by f(x)=(1)x+(2). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(-9, -7), (-8, -6), (-7, -5)}

For every input in D, list (x,f(x)). The graph is {(-9, -7), (-8, -6), (-7, -5)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0054/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 55. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={-8, -7, -6} and f:D→R is given by f(x)=(2)x+(-1). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(-8, -17), (-7, -15), (-6, -13)}

For every input in D, list (x,f(x)). The graph is {(-8, -17), (-7, -15), (-6, -13)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0055/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 56. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={-7, -6, -5} and f:D→R is given by f(x)=(-2)x+(0). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(-7, 14), (-6, 12), (-5, 10)}

For every input in D, list (x,f(x)). The graph is {(-7, 14), (-6, 12), (-5, 10)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0056/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 57. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={-6, -5, -4} and f:D→R is given by f(x)=(-1)x+(1). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(-6, 7), (-5, 6), (-4, 5)}

For every input in D, list (x,f(x)). The graph is {(-6, 7), (-5, 6), (-4, 5)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0057/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 58. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={-5, -4, -3} and f:D→R is given by f(x)=(0)x+(2). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(-5, 2), (-4, 2), (-3, 2)}

For every input in D, list (x,f(x)). The graph is {(-5, 2), (-4, 2), (-3, 2)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0058/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 59. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={-4, -3, -2} and f:D→R is given by f(x)=(1)x+(-1). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(-4, -5), (-3, -4), (-2, -3)}

For every input in D, list (x,f(x)). The graph is {(-4, -5), (-3, -4), (-2, -3)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0059/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 60. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={-3, -2, -1} and f:D→R is given by f(x)=(2)x+(0). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(-3, -6), (-2, -4), (-1, -2)}

For every input in D, list (x,f(x)). The graph is {(-3, -6), (-2, -4), (-1, -2)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0060/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 61. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={-2, -1, 0} and f:D→R is given by f(x)=(-2)x+(1). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(-2, 5), (-1, 3), (0, 1)}

For every input in D, list (x,f(x)). The graph is {(-2, 5), (-1, 3), (0, 1)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0061/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 62. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={-1, 0, 1} and f:D→R is given by f(x)=(-1)x+(2). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(-1, 3), (0, 2), (1, 1)}

For every input in D, list (x,f(x)). The graph is {(-1, 3), (0, 2), (1, 1)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0062/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 63. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={0, 1, 2} and f:D→R is given by f(x)=(0)x+(-1). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(0, -1), (1, -1), (2, -1)}

For every input in D, list (x,f(x)). The graph is {(0, -1), (1, -1), (2, -1)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0063/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 64. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={1, 2, 3} and f:D→R is given by f(x)=(1)x+(0). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(1, 1), (2, 2), (3, 3)}

For every input in D, list (x,f(x)). The graph is {(1, 1), (2, 2), (3, 3)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0064/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 65. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={2, 3, 4} and f:D→R is given by f(x)=(2)x+(1). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(2, 5), (3, 7), (4, 9)}

For every input in D, list (x,f(x)). The graph is {(2, 5), (3, 7), (4, 9)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0065/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 66. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={3, 4, 5} and f:D→R is given by f(x)=(-2)x+(2). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(3, -4), (4, -6), (5, -8)}

For every input in D, list (x,f(x)). The graph is {(3, -4), (4, -6), (5, -8)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0066/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 67. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={4, 5, 6} and f:D→R is given by f(x)=(-1)x+(-1). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(4, -5), (5, -6), (6, -7)}

For every input in D, list (x,f(x)). The graph is {(4, -5), (5, -6), (6, -7)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0067/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 68. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={5, 6, 7} and f:D→R is given by f(x)=(0)x+(0). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(5, 0), (6, 0), (7, 0)}

For every input in D, list (x,f(x)). The graph is {(5, 0), (6, 0), (7, 0)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0068/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 69. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={6, 7, 8} and f:D→R is given by f(x)=(1)x+(1). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(6, 7), (7, 8), (8, 9)}

For every input in D, list (x,f(x)). The graph is {(6, 7), (7, 8), (8, 9)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0069/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 70. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={7, 8, 9} and f:D→R is given by f(x)=(2)x+(2). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(7, 16), (8, 18), (9, 20)}

For every input in D, list (x,f(x)). The graph is {(7, 16), (8, 18), (9, 20)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0070/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 71. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={8, 9, 10} and f:D→R is given by f(x)=(-2)x+(-1). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(8, -17), (9, -19), (10, -21)}

For every input in D, list (x,f(x)). The graph is {(8, -17), (9, -19), (10, -21)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0071/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 72. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={9, 10, 11} and f:D→R is given by f(x)=(-1)x+(0). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(9, -9), (10, -10), (11, -11)}

For every input in D, list (x,f(x)). The graph is {(9, -9), (10, -10), (11, -11)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0072/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 73. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={10, 11, 12} and f:D→R is given by f(x)=(0)x+(1). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(10, 1), (11, 1), (12, 1)}

For every input in D, list (x,f(x)). The graph is {(10, 1), (11, 1), (12, 1)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0073/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 74. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={11, 12, 13} and f:D→R is given by f(x)=(1)x+(2). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(11, 13), (12, 14), (13, 15)}

For every input in D, list (x,f(x)). The graph is {(11, 13), (12, 14), (13, 15)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0074/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 75. Listing a Finite Function Graph

In a fixed Cartesian coordinate system, D={12, 13, 14} and f:D→R is given by f(x)=(2)x+(-1). List the complete graph in increasing order of first coordinate, listing identical points once.

View answer and explanation{(12, 23), (13, 25), (14, 27)}

For every input in D, list (x,f(x)). The graph is {(12, 23), (13, 25), (14, 27)}; an empty domain gives the empty graph ∅.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0075/)

Graphs of real-valued functions · qf-function-graph-finite-set · candidate





## 76. Validity of a Finite Total-Function Graph

The declared domain is D=∅ and codomain is B=∅. Is the ordered-pair set ∅ exactly the graph of a total function D→B?

View answer and explanationYes

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is Yes. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0076/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 77. Validity of a Finite Total-Function Graph

The declared domain is D={-27, -26} and codomain is B={-9, -8, -7}. Is the ordered-pair set {(-27, -9)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0077/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 78. Validity of a Finite Total-Function Graph

The declared domain is D={-24, -23} and codomain is B={-8, -7, -6}. Is the ordered-pair set {(-24, -8), (-23, -7), (-24, -6)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0078/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 79. Validity of a Finite Total-Function Graph

The declared domain is D={-21, -20} and codomain is B={-7, -6, -5}. Is the ordered-pair set {(-21, -7), (-20, 33)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0079/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 80. Validity of a Finite Total-Function Graph

The declared domain is D={-18, -17} and codomain is B={-6, -5, -4}. Is the ordered-pair set {(-18, -6), (-17, -5), (-16, -6)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0080/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 81. Validity of a Finite Total-Function Graph

The declared domain is D={-15, -14} and codomain is B={-5, -4, -3}. Is the ordered-pair set {(-15, -5), (-14, -4)} exactly the graph of a total function D→B?

View answer and explanationYes

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is Yes. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0081/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 82. Validity of a Finite Total-Function Graph

The declared domain is D={-12, -11} and codomain is B={-4, -3, -2}. Is the ordered-pair set {(-12, -4)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0082/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 83. Validity of a Finite Total-Function Graph

The declared domain is D={-9, -8} and codomain is B={-3, -2, -1}. Is the ordered-pair set {(-9, -3), (-8, -2), (-9, -1)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0083/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 84. Validity of a Finite Total-Function Graph

The declared domain is D={-6, -5} and codomain is B={-2, -1, 0}. Is the ordered-pair set {(-6, -2), (-5, 38)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0084/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 85. Validity of a Finite Total-Function Graph

The declared domain is D={-3, -2} and codomain is B={-1, 0, 1}. Is the ordered-pair set {(-3, -1), (-2, 0), (-1, -1)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0085/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 86. Validity of a Finite Total-Function Graph

The declared domain is D={0, 1} and codomain is B={0, 1, 2}. Is the ordered-pair set {(0, 0), (1, 1)} exactly the graph of a total function D→B?

View answer and explanationYes

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is Yes. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0086/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 87. Validity of a Finite Total-Function Graph

The declared domain is D={3, 4} and codomain is B={1, 2, 3}. Is the ordered-pair set {(3, 1)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0087/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 88. Validity of a Finite Total-Function Graph

The declared domain is D={6, 7} and codomain is B={2, 3, 4}. Is the ordered-pair set {(6, 2), (7, 3), (6, 4)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0088/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 89. Validity of a Finite Total-Function Graph

The declared domain is D={9, 10} and codomain is B={3, 4, 5}. Is the ordered-pair set {(9, 3), (10, 43)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0089/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 90. Validity of a Finite Total-Function Graph

The declared domain is D={12, 13} and codomain is B={4, 5, 6}. Is the ordered-pair set {(12, 4), (13, 5), (14, 4)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0090/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 91. Validity of a Finite Total-Function Graph

The declared domain is D={15, 16} and codomain is B={5, 6, 7}. Is the ordered-pair set {(15, 5), (16, 6)} exactly the graph of a total function D→B?

View answer and explanationYes

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is Yes. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0091/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 92. Validity of a Finite Total-Function Graph

The declared domain is D={18, 19} and codomain is B={6, 7, 8}. Is the ordered-pair set {(18, 6)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0092/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 93. Validity of a Finite Total-Function Graph

The declared domain is D={21, 22} and codomain is B={7, 8, 9}. Is the ordered-pair set {(21, 7), (22, 8), (21, 9)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0093/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 94. Validity of a Finite Total-Function Graph

The declared domain is D={24, 25} and codomain is B={8, 9, 10}. Is the ordered-pair set {(24, 8), (25, 48)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0094/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 95. Validity of a Finite Total-Function Graph

The declared domain is D={27, 28} and codomain is B={9, 10, 11}. Is the ordered-pair set {(27, 9), (28, 10), (29, 9)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0095/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 96. Validity of a Finite Total-Function Graph

The declared domain is D={30, 31} and codomain is B={10, 11, 12}. Is the ordered-pair set {(30, 10), (31, 11)} exactly the graph of a total function D→B?

View answer and explanationYes

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is Yes. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0096/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 97. Validity of a Finite Total-Function Graph

The declared domain is D={33, 34} and codomain is B={11, 12, 13}. Is the ordered-pair set {(33, 11)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0097/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 98. Validity of a Finite Total-Function Graph

The declared domain is D={36, 37} and codomain is B={12, 13, 14}. Is the ordered-pair set {(36, 12), (37, 13), (36, 14)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0098/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 99. Validity of a Finite Total-Function Graph

The declared domain is D={39, 40} and codomain is B={13, 14, 15}. Is the ordered-pair set {(39, 13), (40, 53)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0099/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate





## 100. Validity of a Finite Total-Function Graph

The declared domain is D={42, 43} and codomain is B={14, 15, 16}. Is the ordered-pair set {(42, 14), (43, 15), (44, 14)} exactly the graph of a total function D→B?

View answer and explanationNo

Check exactly one output in B for every input in D and exclude points outside D; identical repeated pairs represent the same set element. The answer is No. At most one point per vertical line alone does not establish totality on D.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r06-function-graph-0100/)

Graphs of real-valued functions · qf-function-graph-table-validity · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261003-r06-function-graph-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261003-r06-function-graph-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261003-r06-function-graph-foundations/validation-report.json)