Real-Valued Function Graph Foundations

No

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.

No

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.

Yes

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.

No

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.

No

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.

Yes

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.

No

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.

No

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.

Yes

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.

No

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.

No

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.

Yes

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.

No

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.

No

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.

Yes

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.

No

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.

No

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.

Yes

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.

No

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.

No

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.

Yes

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.

No

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.

No

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.

Yes

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.

No

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.

(-12, 23)

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

(-10, 10)

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

(-8, 1)

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

(-9, -7)

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

(-7, -15)

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

(-5, 10)

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

(-6, 7)

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

(-4, 2)

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

(-2, -3)

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

(-3, -6)

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

(-1, 3)

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

(1, 1)

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

(0, -1)

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

(2, 2)

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

(4, 9)

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

(3, -4)

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

(5, -6)

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

(7, 0)

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

(6, 7)

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

(8, 18)

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

(10, -21)

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

(9, -9)

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

(11, 1)

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

(13, 15)

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

(12, 23)

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

∅

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

{(0, 0)}

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

{(-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 ∅.

{(-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 ∅.

{(-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 ∅.

{(-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 ∅.

{(-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 ∅.

{(-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 ∅.

{(-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 ∅.

{(-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 ∅.

{(-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 ∅.

{(-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 ∅.

{(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 ∅.

{(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 ∅.

{(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 ∅.

{(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 ∅.

{(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 ∅.

{(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 ∅.

{(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 ∅.

{(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 ∅.

{(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 ∅.

{(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 ∅.

{(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 ∅.

{(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 ∅.

{(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 ∅.

Yes

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.

No

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.

No

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.

No

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.

No

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.

Yes

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.

No

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.

No

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.

No

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.

No

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.

Yes

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.

No

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.

No

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.

No

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.

No

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.

Yes

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.

No

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.

No

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.

No

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.

No

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.

Yes

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.

No

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.

No

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.

No

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.

No

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.