Free Printable Graphing Rational Functions Review

1.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

2.

What is the horizontal asymptote?

(a)

Choose from the below words

x = 2

y = 2

x =-2

y=-2

3.

What is the vertical asymptote?

a)

x = 2

b)

y = 2

c)

x = 1

d)

y = 1

4.

The rational function, $y=\frac{1}{x-5}$ is undefined at...

a)

x = 1

b)

x = 5

c)

x = -5

d)

x = 0

5.

The rational function, $y=\frac{1}{x+7}$ has a vertical asymptote at...

a)

y = -7

b)

x = 7

c)

y = 0

d)

x = -7

6.

This rational function is undefined at...

a)

x = 4

b)

x = -4

c)

x = 0

d)

x = 5

7.

Which rational function has a vertical asymptote at x = -3

a)

$y=\frac{1}{x-3}$

b)

$y=\frac{1}{x+3}$

c)

$y=\frac{1}{3}$

d)

$y=\frac{3}{x}$

8.

What is the equation of the rational function graphed?

a)

$f\left(x\right)=\frac{1}{x-2}$

b)

$f\left(x\right)=\frac{1}{x+2}$

c)

$f\left(x\right)=\frac{1}{x}+2$

d)

$f\left(x\right)=\frac{1}{x}-2$

9.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1

d)

y = 9

10.

The rational function, $f\left(x\right)=3+\frac{2}{x-4}$ has a horizontal asymptote at...

a)

y = -4

b)

y = 2

c)

y = 3

d)

y= 4

11.

What's the horizontal asymptote of the function?

$f\left(x\right)=\frac{3x+2}{x^2+1}$

a)

y = 3

b)

No horizontal asymptote

c)

y = 0

d)

y = 2

12.

a)

x=3 and x=5

b)

x=3

c)

x=5

d)

x=0

13.

a)

Asy: x=-4 H:x=-2

b)

Asy: x=-4 H:x=2

c)

Asy: x=-5 H:x=-4

d)

Asy: x=4 H:x=-2

14.

a)

VA:x=2 HA:y=3

b)

VA:x=2 HA:y=-3

c)

VA:x=-2 HA:y=-3

d)

VA:x=-2 HA:y=3

15.

a)

(−∞,∞)

b)

(−∞,0)(0,∞)

c)

(−∞,−2)(−2,∞)

d)

(−∞,∞)(∞,∞)

16.

a)

x=3

b)

x=1

c)

x=-3

d)

x=-2

17.

a)

x=1, x=-3

b)

x=-4

c)

x=1

d)

x=-4,x=-3

18.

a)

x=1

b)

none

c)

y=1

d)

y=0

19.

a)

A

b)

B

c)

C

d)

D

20.

a)

A

b)

B

c)

C

d)

D

21.

a)

The function's range is (−∞, 0) ∪ (0, ∞)

b)

The function's domain is (−∞, 2) ∪ (2, ∞)

c)

It's a rational function that has been shifted left 2 units, and down 1 unit.

d)

It is a reflected rational function

22.

a)

None

b)

x = -4

c)

x = 3

d)

x = 4

23.

What creates a hole in the graph of a rational function?

a)

Crossing the x-axis

b)

Crossing the y-axis

c)

Crossing a vertical asymptote.

d)

A factor that cancels out.

24.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

25.

How is this function transformed from the parent function?

a)

Translated left and up

b)

Translated right and up

c)

Translated left and down

d)

Translated right and down

26.

What is the RANGE?

a)

$\left(-\infty,-3\right)U\left(-3,\infty\right)$

b)

$\left(-\infty,1\right)U\left(1,\infty\right)$

c)

$\left(-\infty,-3\right)U\ \left(-3,\ 1\right)\ U\left(1,\infty\right)$

d)

All Real Numbers

27.

What is the DOMAIN?

a)

$\left(-\infty,-3\right)U\left(-3,\infty\right)$

b)

$\left(-\infty,1\right)U\left(1,\infty\right)$

c)

$\left(-\infty,-3\right)U\ \left(-3,\ 1\right)\ U\left(1,\infty\right)$

d)

All Real Numbers

28.

What is/are the vertical asymptote(s)?

a)

x=-2

b)

x=2 and x=3

c)

x=-3

d)

x=3

29.

What is the hole?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

30.

Find the horizontal asymptote.

a)

None

b)

y = 0

c)

y = -1/3

d)

y = -3

31.

Find the vertical asymptotes and holes of the function.

a)

Holes: None;

VA: x = 1, -3

b)

Holes: x = -3;

VA: x = 1

c)

Holes: x = -3, 1

VA: None

d)

Holes: x = 1

VA: x = -3

32.

Find the horizontal asymptote.

a)

y = -2

b)

none

c)

y = 0

d)

y = 1/2

33.

What's the vertical asymptote of the function?

a)

x = 5

b)

x = 0

c)

x =5 , x = -5

d)

x = 25

34.

What is the equation of the horizontal asymptote?

a)

y = 0

b)

y = -2

c)

y = 2

d)

There isn't one

35.

$h\left(x\right)=\frac{x\left(x-3\right)\left(x-6\right)\left(x+5\right)}{3x\left(x+3\right)\left(x-6\right)\left(x+7\right)}$

Identify the vertical asymptote(s).

**Select all that apply**

a)

x=0

b)

x=-3

c)

x=6

d)

x=-7

e)

x=3

36.

$h\left(x\right)=\frac{x\left(x-3\right)\left(x-6\right)\left(x+3\right)}{3x\left(x+3\right)\left(x-6\right)\left(x+7\right)}$

Identify the x-value of the hole(s).

**Select all that apply**

a)

x=0

b)

x=-3

c)

x=6

d)

x=-7

e)

x=3

37.

$f\left(x\right)=\frac{\left(x+7\right)\left(x-3\right)\left(x+1\right)}{\left(x-3\right)\left(x-5\right)}$

Select all of the true statements.

a)

A hole occurs where x=3

b)

vertical asymptote at x=3

c)

vertical asymptote at x=5

d)

A hole occurs where x=5

38.

What is the x-value of the hole? $g\left(x\right)=\frac{\left(x-2\right)\left(x+6\right)}{\left(x+2\right)\left(x-2\right)}$

a)

2

b)

-2

c)

-6

d)

6

39.

Does this function have any vertical asymptotes? If so, what are their equations? $y=\frac{\left(x+3\right)\left(x-4\right)\left(x+7\right)}{\left(x-4\right)}$

a)

No vertical asymptotes.

b)

One vertical asymptote: x = 4

c)

Two vertical asymptotes: x = -3 and x = -7

d)

Three vertical asymptotes: x = -3, x = 4, and x = -7

40.

Where is there a hole on the graph of the function?

a)

$\left(2,0\right)$

b)

$\left(-2,\ -\frac{4}{7}\right)$

c)

There are no holes.

d)

$\left(5,-7\right)$

41.

What is the horizontal asymptote of this function?

a)

y=2

b)

x=1/2

c)

y=1

d)

y=1/2

42.

Find the horizontal asymptote.

a)

None

b)

y=-2

c)

y=2

d)

y=0

Graphing Rational Functions Review

Total questions: 42

Worksheet time: 4hrs 30mins

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