Affine Function Foundations

45

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

31

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

19

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

9

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

1

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

-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.

-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.

-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.

-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.

11

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

6

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

3

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

2

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

3

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

-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.

4

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

11

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

20

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

-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.

-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.

-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.

-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.

-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.

10

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

24

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

-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.

11/2

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.

-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.

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.

-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.

7/6

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.

-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.

5/2

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.

-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.

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.

-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.

1/6

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.

0/1

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.

-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.

2/3

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.

-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.

4/5

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.

-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.

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.

-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.

8/3

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.

-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.

2/1

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.

-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.

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.

R

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.

∅

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.

{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.

{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.

{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.

{-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.

{-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.

{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.

{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.

{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.

{-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.

{-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.

{-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.

{-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.

{-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.

{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.

{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.

{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.

{-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.

{-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.

{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.

{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.

{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.

{-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.

{-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.

Yes

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

No

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

Yes

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

No

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

Yes

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

No

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

Yes

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

No

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

Yes

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

No

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

Yes

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

No

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

Yes

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

No

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

Yes

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

No

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

Yes

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

No

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

Yes

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

No

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

Yes

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

No

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

Yes

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

No

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

Yes

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