# Affine Function 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-r05-linear-function-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. Exact Affine-Function Evaluation

Over R, f(x)=(-12)x+(-3). Compute f(-4) exactly.

View answer and explanation45

Multiply the input by the slope, then add the intercept: f(-4)=45. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0001/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 2. Exact Affine-Function Evaluation

Over R, f(x)=(-11)x+(-2). Compute f(-3) exactly.

View answer and explanation31

Multiply the input by the slope, then add the intercept: f(-3)=31. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0002/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 3. Exact Affine-Function Evaluation

Over R, f(x)=(-10)x+(-1). Compute f(-2) exactly.

View answer and explanation19

Multiply the input by the slope, then add the intercept: f(-2)=19. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0003/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 4. Exact Affine-Function Evaluation

Over R, f(x)=(-9)x+(0). Compute f(-1) exactly.

View answer and explanation9

Multiply the input by the slope, then add the intercept: f(-1)=9. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0004/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 5. Exact Affine-Function Evaluation

Over R, f(x)=(-8)x+(1). Compute f(0) exactly.

View answer and explanation1

Multiply the input by the slope, then add the intercept: f(0)=1. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0005/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 6. Exact Affine-Function Evaluation

Over R, f(x)=(-7)x+(2). Compute f(1) exactly.

View answer and explanation-5

Multiply the input by the slope, then add the intercept: f(1)=-5. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0006/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 7. Exact Affine-Function Evaluation

Over R, f(x)=(-6)x+(3). Compute f(2) exactly.

View answer and explanation-9

Multiply the input by the slope, then add the intercept: f(2)=-9. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0007/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 8. Exact Affine-Function Evaluation

Over R, f(x)=(-5)x+(-3). Compute f(3) exactly.

View answer and explanation-18

Multiply the input by the slope, then add the intercept: f(3)=-18. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0008/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 9. Exact Affine-Function Evaluation

Over R, f(x)=(-4)x+(-2). Compute f(4) exactly.

View answer and explanation-18

Multiply the input by the slope, then add the intercept: f(4)=-18. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0009/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 10. Exact Affine-Function Evaluation

Over R, f(x)=(-3)x+(-1). Compute f(-4) exactly.

View answer and explanation11

Multiply the input by the slope, then add the intercept: f(-4)=11. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0010/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 11. Exact Affine-Function Evaluation

Over R, f(x)=(-2)x+(0). Compute f(-3) exactly.

View answer and explanation6

Multiply the input by the slope, then add the intercept: f(-3)=6. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0011/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 12. Exact Affine-Function Evaluation

Over R, f(x)=(-1)x+(1). Compute f(-2) exactly.

View answer and explanation3

Multiply the input by the slope, then add the intercept: f(-2)=3. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0012/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 13. Exact Affine-Function Evaluation

Over R, f(x)=(0)x+(2). Compute f(-1) exactly.

View answer and explanation2

Multiply the input by the slope, then add the intercept: f(-1)=2. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0013/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 14. Exact Affine-Function Evaluation

Over R, f(x)=(1)x+(3). Compute f(0) exactly.

View answer and explanation3

Multiply the input by the slope, then add the intercept: f(0)=3. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0014/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 15. Exact Affine-Function Evaluation

Over R, f(x)=(2)x+(-3). Compute f(1) exactly.

View answer and explanation-1

Multiply the input by the slope, then add the intercept: f(1)=-1. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0015/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 16. Exact Affine-Function Evaluation

Over R, f(x)=(3)x+(-2). Compute f(2) exactly.

View answer and explanation4

Multiply the input by the slope, then add the intercept: f(2)=4. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0016/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 17. Exact Affine-Function Evaluation

Over R, f(x)=(4)x+(-1). Compute f(3) exactly.

View answer and explanation11

Multiply the input by the slope, then add the intercept: f(3)=11. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0017/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 18. Exact Affine-Function Evaluation

Over R, f(x)=(5)x+(0). Compute f(4) exactly.

View answer and explanation20

Multiply the input by the slope, then add the intercept: f(4)=20. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0018/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 19. Exact Affine-Function Evaluation

Over R, f(x)=(6)x+(1). Compute f(-4) exactly.

View answer and explanation-23

Multiply the input by the slope, then add the intercept: f(-4)=-23. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0019/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 20. Exact Affine-Function Evaluation

Over R, f(x)=(7)x+(2). Compute f(-3) exactly.

View answer and explanation-19

Multiply the input by the slope, then add the intercept: f(-3)=-19. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0020/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 21. Exact Affine-Function Evaluation

Over R, f(x)=(8)x+(3). Compute f(-2) exactly.

View answer and explanation-13

Multiply the input by the slope, then add the intercept: f(-2)=-13. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0021/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 22. Exact Affine-Function Evaluation

Over R, f(x)=(9)x+(-3). Compute f(-1) exactly.

View answer and explanation-12

Multiply the input by the slope, then add the intercept: f(-1)=-12. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0022/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 23. Exact Affine-Function Evaluation

Over R, f(x)=(10)x+(-2). Compute f(0) exactly.

View answer and explanation-2

Multiply the input by the slope, then add the intercept: f(0)=-2. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0023/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 24. Exact Affine-Function Evaluation

Over R, f(x)=(11)x+(-1). Compute f(1) exactly.

View answer and explanation10

Multiply the input by the slope, then add the intercept: f(1)=10. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0024/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 25. Exact Affine-Function Evaluation

Over R, f(x)=(12)x+(0). Compute f(2) exactly.

View answer and explanation24

Multiply the input by the slope, then add the intercept: f(2)=24. Constant functions with m=0 also belong to the affine family.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0025/)

Affine functions and degree-one functions · qf-affine-exact-evaluation · candidate





## 26. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (-12, -2) and (-11, -14), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation-12/1

Use (y_2−y_1)/(x_2−x_1) to obtain -12/1. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0026/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 27. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (-11, -1) and (-13, -12), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation11/2

Use (y_2−y_1)/(x_2−x_1) to obtain 11/2. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0027/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 28. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (-10, 0) and (-7, -10), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation-10/3

Use (y_2−y_1)/(x_2−x_1) to obtain -10/3. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0028/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 29. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (-9, 1) and (-13, -8), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation9/4

Use (y_2−y_1)/(x_2−x_1) to obtain 9/4. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0029/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 30. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (-8, 2) and (-3, -6), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation-8/5

Use (y_2−y_1)/(x_2−x_1) to obtain -8/5. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0030/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 31. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (-7, -2) and (-13, -9), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation7/6

Use (y_2−y_1)/(x_2−x_1) to obtain 7/6. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0031/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 32. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (-6, -1) and (-5, -7), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation-6/1

Use (y_2−y_1)/(x_2−x_1) to obtain -6/1. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0032/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 33. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (-5, 0) and (-7, -5), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation5/2

Use (y_2−y_1)/(x_2−x_1) to obtain 5/2. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0033/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 34. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (-4, 1) and (-1, -3), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation-4/3

Use (y_2−y_1)/(x_2−x_1) to obtain -4/3. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0034/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 35. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (-3, 2) and (-7, -1), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation3/4

Use (y_2−y_1)/(x_2−x_1) to obtain 3/4. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0035/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 36. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (-2, -2) and (3, -4), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation-2/5

Use (y_2−y_1)/(x_2−x_1) to obtain -2/5. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0036/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 37. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (-1, -1) and (-7, -2), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation1/6

Use (y_2−y_1)/(x_2−x_1) to obtain 1/6. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0037/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 38. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (0, 0) and (1, 0), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation0/1

Use (y_2−y_1)/(x_2−x_1) to obtain 0/1. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0038/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 39. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (1, 1) and (-1, 2), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation-1/2

Use (y_2−y_1)/(x_2−x_1) to obtain -1/2. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0039/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 40. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (2, 2) and (5, 4), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation2/3

Use (y_2−y_1)/(x_2−x_1) to obtain 2/3. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0040/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 41. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (3, -2) and (-1, 1), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation-3/4

Use (y_2−y_1)/(x_2−x_1) to obtain -3/4. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0041/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 42. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (4, -1) and (9, 3), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation4/5

Use (y_2−y_1)/(x_2−x_1) to obtain 4/5. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0042/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 43. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (5, 0) and (-1, 5), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation-5/6

Use (y_2−y_1)/(x_2−x_1) to obtain -5/6. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0043/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 44. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (6, 1) and (7, 7), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation6/1

Use (y_2−y_1)/(x_2−x_1) to obtain 6/1. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0044/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 45. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (7, 2) and (5, 9), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation-7/2

Use (y_2−y_1)/(x_2−x_1) to obtain -7/2. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0045/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 46. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (8, -2) and (11, 6), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation8/3

Use (y_2−y_1)/(x_2−x_1) to obtain 8/3. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0046/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 47. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (9, -1) and (5, 8), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation-9/4

Use (y_2−y_1)/(x_2−x_1) to obtain -9/4. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0047/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 48. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (10, 0) and (15, 10), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation2/1

Use (y_2−y_1)/(x_2−x_1) to obtain 2/1. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0048/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 49. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (11, 1) and (5, 12), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation-11/6

Use (y_2−y_1)/(x_2−x_1) to obtain -11/6. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0049/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 50. Two-Point Slope of an Affine Graph

Over the reals, an affine-function graph contains (12, 2) and (13, 14), with distinct first coordinates. Find the slope as a reduced fraction with positive denominator.

View answer and explanation12/1

Use (y_2−y_1)/(x_2−x_1) to obtain 12/1. The denominator is nonzero; this formula does not give the slope of a vertical line.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0050/)

Affine functions and degree-one functions · qf-affine-two-point-slope · candidate





## 51. Complete Zero Set of an Affine Function

Over R, f(x)=(0)x+(0). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanationR

The zero set is R. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0051/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 52. Complete Zero Set of an Affine Function

Over R, f(x)=(0)x+(3). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation∅

The zero set is ∅. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0052/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 53. Complete Zero Set of an Affine Function

Over R, f(x)=(-10)x+(0). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{0/1}

The zero set is {0/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0053/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 54. Complete Zero Set of an Affine Function

Over R, f(x)=(-9)x+(1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{1/9}

The zero set is {1/9}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0054/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 55. Complete Zero Set of an Affine Function

Over R, f(x)=(-8)x+(2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{1/4}

The zero set is {1/4}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0055/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 56. Complete Zero Set of an Affine Function

Over R, f(x)=(-7)x+(-2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{-2/7}

The zero set is {-2/7}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0056/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 57. Complete Zero Set of an Affine Function

Over R, f(x)=(-6)x+(-1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{-1/6}

The zero set is {-1/6}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0057/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 58. Complete Zero Set of an Affine Function

Over R, f(x)=(-5)x+(0). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{0/1}

The zero set is {0/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0058/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 59. Complete Zero Set of an Affine Function

Over R, f(x)=(-4)x+(1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{1/4}

The zero set is {1/4}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0059/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 60. Complete Zero Set of an Affine Function

Over R, f(x)=(-3)x+(2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{2/3}

The zero set is {2/3}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0060/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 61. Complete Zero Set of an Affine Function

Over R, f(x)=(-2)x+(-2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{-1/1}

The zero set is {-1/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0061/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 62. Complete Zero Set of an Affine Function

Over R, f(x)=(-1)x+(-1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{-1/1}

The zero set is {-1/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0062/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 63. Complete Zero Set of an Affine Function

Over R, f(x)=(1)x+(4). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{-4/1}

The zero set is {-4/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0063/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 64. Complete Zero Set of an Affine Function

Over R, f(x)=(1)x+(1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{-1/1}

The zero set is {-1/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0064/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 65. Complete Zero Set of an Affine Function

Over R, f(x)=(2)x+(2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{-1/1}

The zero set is {-1/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0065/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 66. Complete Zero Set of an Affine Function

Over R, f(x)=(3)x+(-2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{2/3}

The zero set is {2/3}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0066/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 67. Complete Zero Set of an Affine Function

Over R, f(x)=(4)x+(-1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{1/4}

The zero set is {1/4}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0067/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 68. Complete Zero Set of an Affine Function

Over R, f(x)=(5)x+(0). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{0/1}

The zero set is {0/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0068/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 69. Complete Zero Set of an Affine Function

Over R, f(x)=(6)x+(1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{-1/6}

The zero set is {-1/6}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0069/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 70. Complete Zero Set of an Affine Function

Over R, f(x)=(7)x+(2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{-2/7}

The zero set is {-2/7}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0070/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 71. Complete Zero Set of an Affine Function

Over R, f(x)=(8)x+(-2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{1/4}

The zero set is {1/4}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0071/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 72. Complete Zero Set of an Affine Function

Over R, f(x)=(9)x+(-1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{1/9}

The zero set is {1/9}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0072/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 73. Complete Zero Set of an Affine Function

Over R, f(x)=(10)x+(0). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{0/1}

The zero set is {0/1}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0073/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 74. Complete Zero Set of an Affine Function

Over R, f(x)=(11)x+(1). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{-1/11}

The zero set is {-1/11}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0074/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 75. Complete Zero Set of an Affine Function

Over R, f(x)=(12)x+(2). Find its complete zero set, using R, ∅, or a set of reduced rational numbers.

View answer and explanation{-1/6}

The zero set is {-1/6}. For m≠0, −b/m is the unique zero; for m=0 and b=0 every real input is a zero, while for m=0 and b≠0 there are none.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0075/)

Affine functions and degree-one functions · qf-affine-zero-set · candidate





## 76. Affine Functions at One Input

Over R, f(x)=(1)x+(2) and g(x)=(1)x+(2). At the single input x=0, are f(x) and g(x) equal?

View answer and explanationYes

f(0)=2 and g(0)=2, so the answer is Yes. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0076/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 77. Affine Functions at One Input

Over R, f(x)=(-11)x+(-1) and g(x)=(-10)x+(2). At the single input x=-2, are f(x) and g(x) equal?

View answer and explanationNo

f(-2)=21 and g(-2)=22, so the answer is No. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0077/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 78. Affine Functions at One Input

Over R, f(x)=(-10)x+(0) and g(x)=(-9)x+(1). At the single input x=-1, are f(x) and g(x) equal?

View answer and explanationYes

f(-1)=10 and g(-1)=10, so the answer is Yes. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0078/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 79. Affine Functions at One Input

Over R, f(x)=(-9)x+(1) and g(x)=(-8)x+(2). At the single input x=0, are f(x) and g(x) equal?

View answer and explanationNo

f(0)=1 and g(0)=2, so the answer is No. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0079/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 80. Affine Functions at One Input

Over R, f(x)=(-8)x+(2) and g(x)=(-7)x+(1). At the single input x=1, are f(x) and g(x) equal?

View answer and explanationYes

f(1)=-6 and g(1)=-6, so the answer is Yes. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0080/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 81. Affine Functions at One Input

Over R, f(x)=(-7)x+(-2) and g(x)=(-6)x+(-3). At the single input x=2, are f(x) and g(x) equal?

View answer and explanationNo

f(2)=-16 and g(2)=-15, so the answer is No. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0081/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 82. Affine Functions at One Input

Over R, f(x)=(-6)x+(-1) and g(x)=(-5)x+(-4). At the single input x=3, are f(x) and g(x) equal?

View answer and explanationYes

f(3)=-19 and g(3)=-19, so the answer is Yes. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0082/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 83. Affine Functions at One Input

Over R, f(x)=(-5)x+(0) and g(x)=(-4)x+(4). At the single input x=-3, are f(x) and g(x) equal?

View answer and explanationNo

f(-3)=15 and g(-3)=16, so the answer is No. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0083/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 84. Affine Functions at One Input

Over R, f(x)=(-4)x+(1) and g(x)=(-3)x+(3). At the single input x=-2, are f(x) and g(x) equal?

View answer and explanationYes

f(-2)=9 and g(-2)=9, so the answer is Yes. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0084/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 85. Affine Functions at One Input

Over R, f(x)=(-3)x+(2) and g(x)=(-2)x+(4). At the single input x=-1, are f(x) and g(x) equal?

View answer and explanationNo

f(-1)=5 and g(-1)=6, so the answer is No. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0085/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 86. Affine Functions at One Input

Over R, f(x)=(-2)x+(-2) and g(x)=(-1)x+(-2). At the single input x=0, are f(x) and g(x) equal?

View answer and explanationYes

f(0)=-2 and g(0)=-2, so the answer is Yes. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0086/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 87. Affine Functions at One Input

Over R, f(x)=(-1)x+(-1) and g(x)=(0)x+(-1). At the single input x=1, are f(x) and g(x) equal?

View answer and explanationNo

f(1)=-2 and g(1)=-1, so the answer is No. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0087/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 88. Affine Functions at One Input

Over R, f(x)=(0)x+(0) and g(x)=(1)x+(-2). At the single input x=2, are f(x) and g(x) equal?

View answer and explanationYes

f(2)=0 and g(2)=0, so the answer is Yes. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0088/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 89. Affine Functions at One Input

Over R, f(x)=(1)x+(1) and g(x)=(2)x+(-1). At the single input x=3, are f(x) and g(x) equal?

View answer and explanationNo

f(3)=4 and g(3)=5, so the answer is No. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0089/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 90. Affine Functions at One Input

Over R, f(x)=(2)x+(2) and g(x)=(3)x+(5). At the single input x=-3, are f(x) and g(x) equal?

View answer and explanationYes

f(-3)=-4 and g(-3)=-4, so the answer is Yes. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0090/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 91. Affine Functions at One Input

Over R, f(x)=(3)x+(-2) and g(x)=(4)x+(1). At the single input x=-2, are f(x) and g(x) equal?

View answer and explanationNo

f(-2)=-8 and g(-2)=-7, so the answer is No. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0091/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 92. Affine Functions at One Input

Over R, f(x)=(4)x+(-1) and g(x)=(5)x+(0). At the single input x=-1, are f(x) and g(x) equal?

View answer and explanationYes

f(-1)=-5 and g(-1)=-5, so the answer is Yes. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0092/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 93. Affine Functions at One Input

Over R, f(x)=(5)x+(0) and g(x)=(6)x+(1). At the single input x=0, are f(x) and g(x) equal?

View answer and explanationNo

f(0)=0 and g(0)=1, so the answer is No. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0093/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 94. Affine Functions at One Input

Over R, f(x)=(6)x+(1) and g(x)=(7)x+(0). At the single input x=1, are f(x) and g(x) equal?

View answer and explanationYes

f(1)=7 and g(1)=7, so the answer is Yes. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0094/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 95. Affine Functions at One Input

Over R, f(x)=(7)x+(2) and g(x)=(8)x+(1). At the single input x=2, are f(x) and g(x) equal?

View answer and explanationNo

f(2)=16 and g(2)=17, so the answer is No. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0095/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 96. Affine Functions at One Input

Over R, f(x)=(8)x+(-2) and g(x)=(9)x+(-5). At the single input x=3, are f(x) and g(x) equal?

View answer and explanationYes

f(3)=22 and g(3)=22, so the answer is Yes. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0096/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 97. Affine Functions at One Input

Over R, f(x)=(9)x+(-1) and g(x)=(10)x+(3). At the single input x=-3, are f(x) and g(x) equal?

View answer and explanationNo

f(-3)=-28 and g(-3)=-27, so the answer is No. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0097/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 98. Affine Functions at One Input

Over R, f(x)=(10)x+(0) and g(x)=(11)x+(2). At the single input x=-2, are f(x) and g(x) equal?

View answer and explanationYes

f(-2)=-20 and g(-2)=-20, so the answer is Yes. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0098/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 99. Affine Functions at One Input

Over R, f(x)=(11)x+(1) and g(x)=(12)x+(3). At the single input x=-1, are f(x) and g(x) equal?

View answer and explanationNo

f(-1)=-10 and g(-1)=-9, so the answer is No. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0099/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate





## 100. Affine Functions at One Input

Over R, f(x)=(12)x+(2) and g(x)=(13)x+(2). At the single input x=0, are f(x) and g(x) equal?

View answer and explanationYes

f(0)=2 and g(0)=2, so the answer is Yes. Equality at this input does not establish equality on the whole domain.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261003-r05-linear-function-0100/)

Affine functions and degree-one functions · qf-affine-pointwise-comparison · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261003-r05-linear-function-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261003-r05-linear-function-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261003-r05-linear-function-foundations/validation-report.json)