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Unit 5.4 Quiz Review -- Rational Functions & their Graphs

Total questions: 50

Worksheet time: 4hrs 10mins

Name
Class
Date
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 equation that best matches the graph?
a)
A
b)
B
c)
C
d)
D
3.

What is/are the vertical asymptote(s)?

a)

There are no vertical asymptotes

b)

x=5

c)

x=-5

d)

x=-1/2

4.
What are the Vertical Asymptotes of...
a)
x = 0, -5
b)
x=0, 5
c)
x = 2, -7
d)
x = -2, 7
5.
What is the Horizontal Asymptote?
a)
None
b)
y= 0
c)
y= 1
d)
y= 5/4
6.

What is the x-coordinate of the hole?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

7.
Find the horizontal asymptote.
a)
None
b)
y = 0
c)
y = -1/3
d)
y = -3
8.
Which asymptote(s) are determined by looking at the denominator?
a)
vertical
b)
horizontal
c)
slant
d)
none
9.

Determine whether the graph of the function has a vertical asymptote or a hole at x = -1.

a)

Vertical Asymptote

at x = -1

b)

Hole

at x = -1

c)

Neither a VA or a hole at x = -1

d)

Has both a VA and a hole at

x = -1

e)

mmm...donuts

10.

What is/are the x-intercepts of this graph?

a)

(-2,0) and (2,0)

b)

(-2,0) only

c)

(3,0) only

d)

(2,0) and (3,0)

11.
Where is the hole in this graph?
a)

(-3, 2)

b)

(-3, 1/2)

c)

(-5, 0)

d)

There is No Hole

12.

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

a)

Crossing the x-axis

b)

An absence of dirt.

c)

Crossing a vertical asymptote.

d)

A factor that cancels out.

e)

Making donuts...mmm

13.
What is the domain and range?
a)
D : All real number x ≠ -3
R: All real number y≠ 1
b)
D : All real number x ≠ 1
R: All real number y≠ -3
c)
D : All real number x ≠ 3
R: All real number y≠ 1
d)
D : All real number x ≠ -1
R: All real number y≠ 3
14.
What is the horizontal asymptote? 
a)
x = 2
b)
x = 7
c)
y = 2
d)
y = 7
15.

Which function matches this graph?

a)

f(x)=4x−2f\left(x\right)=\frac{4}{x-2}

b)

f(x)=4x+2f\left(x\right)=\frac{4}{x+2}

c)

f(x)=−4x−2f\left(x\right)=\frac{-4}{x-2}

d)

f(x)=−4x+2f\left(x\right)=\frac{-4}{x+2}

16.

What is the end behavior of f(x)=99+9xxf\left(x\right)=\frac{99+9x}{x}  as x gets larger and larger?

a)

The value of the expression gets closer and closer to 0.

b)

The value of the expression gets closer and closer to 1.

c)

The value of the expression gets closer and closer to 9.

d)

The value of the expression gets closer and closer to 99.

17.

Which of the following is NOT a vertical asymptote of the following function?

a)

x = 4

b)

x = -4

c)

x = 2

d)

x = -2

18.

What is the domain for the following function?

a)

All real numbers except 2.

b)

All real numbers except -2.

c)

All real numbers except 4.

d)

All real numbers.

19.

What is the range for the following function?

a)

All real numbers.

b)

All real numbers except for -2.

c)

All real numbers except for 2.

d)

All real numbers exceptt for 4.

20.

What is the equation of the horizontal asymptote?

a)

y = 0

b)

y = -2

c)

y = 2

d)

There isn't one

21.

What is the equation of the vertical asymptote?

a)

x = 0

b)

x = 4

c)

x = -1, x = 4

d)

x = -1

22.

What are the coordinates of the hole, if one exists.

a)

(-1, -2)

b)

(-1, ½)

c)

(-1, -½)

d)

there isn't one

23.

What is the domain?

a)

x ≠ 3

b)

x ≠ -1

c)

x ≠ 3, -1

d)

x ≠ 3, 1

24.

Find the x-intercept(s), if one exists.

a)

(1, 0)

b)

(-1, 0)

c)

(1, 0), (-1, 0)

d)

(0, 0), (1, 0)

25.

What are the coordinates of the y-intercept, if one exists.

a)

(0, 0)

b)

(0, 1)

c)

(0, -1)

d)

there isn't one

26.

What is the equation of the slant asymptote?

a)

y = x + 1

b)

y = x + 2

c)

y = x + 3

d)

y = x

27.

What is the equation of the slant asymptote?

a)

y = x - 4

b)

y = 4x - 4

c)

y = 4x + 16

d)

there isn't one

28.

What are the x and y intercepts?

a)

(4, 0) and (0, -4)

b)

(-4, 0) and (0, -4)

c)

(-4, 0) and (0, 4)

d)

(0, 0) and (0, -4)

29.

What is the equation of the graph?

a)
b)
c)
d)
30.

What is the equation of the graph?

a)
b)
c)
d)
31.

Write an equation for the graph.

a)
b)
c)
d)
32.

Which statements are true for the given rational function. Select all that apply.

a)

The horizontal asymptote is at y = 0.

b)

There is a hole at (6, ¾ ).

c)

The vertical asymptote is at x = -2.

d)

The x and y intercepts are at the origin.

e)

The domain is all real numbers except -2.

33.

Write the equation for the graph.

a)

y=xy=x

b)

y=x2y=x^2

c)

y=1xy=\frac{1}{x}

d)

y=∣x∣y=\left|x\right|

34.
What is the y-intercept?
a)
-1
b)
0
c)
4
d)
None
35.
a)
-1
b)
0
c)
4
d)
None
36.
What is the horizontal asymptote of the function?
a)
y=0
b)
y=1/3
c)
none
37.
A vertical asymptote is found by setting the _________= to zero and solving for x 
a)
Numerator
b)
Denominator
c)
Right side 
d)
Left side
38.

How do you find the y-intercept?

a)

replace all x-values with 0

b)

replace all y-values with 0

c)

set denominator equal to 0

d)

compare the degrees of the numerator and denominator

39.

How do you find the x-intercept?

a)

replace all x-values with 0

b)

replace the y-value with 0 or make the numerator equal 0

c)

set denominator equal to 0

d)

compare the degrees of the numerator and denominator

40.

How do you determine the Horizontal Asymptote?

a)

replace all x-values with 0

b)

replace the y-value with 0 or make the numerator equal 0

c)

set denominator equal to 0

d)

compare the degrees of the numerator and denominator

41.

When finding the H.A., if the numerator degree is greater than the denominator degree, the answer is...

a)

y = 0

b)

none

c)

y = quotient of LC's

d)

What's an H.A.?

42.

When finding the H.A., if the numerator degree is equal to the denominator degree, the answer is...

a)

y = 0

b)

none

c)

y = quotient of LC's

d)

What's an H.A.?

43.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1

d)

y = 9

44.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1/2

d)

y = 1

45.

What's the vertical asymptote of the function?

a)

x = 5

b)

x = 0

c)

x =5 , x = -5

d)

x = 25

46.
What is the X-Intercept?
a)
x= 0
b)
x= 4
c)
x= 5
d)
x= -5
47.
What are the x-intercepts?
a)
x= 2/3
b)
x= 4, x = -2
c)
x= -8, x = 1
d)
x= -4, x = 2
48.
What are the asymptotes?
a)
x=1, x= 2, y =1, y= 2
b)
x= 2, x=-2, y = 1
c)
x=2 y =-1
d)
x=1 y =2, y =-2
49.

What (if any) holes exist?

a)

x=2

b)

x=2 and x=3

c)

x=-3

d)

x=3

50.

Given f(x)=x2+10x+25x2+8x+15f\left(x\right)=\frac{x^2+10x+25}{x^2+8x+15} , which feature DOES NOT exist?

a)

VA

b)

HA

c)

Hole

d)

x-intercept

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