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Worksheets

Key Features of Rational Functions

Total questions: 23

Worksheet time: 1hrs 14mins

Name
Class
Date
1.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 2

d)

y = 4

2.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1/2

d)

y = 1

3.

What's the vertical asymptote of the function?

a)

x = -9

b)

x = 9

c)

x = 3 , x = -3

d)

x = 3

4.

What's the vertical asymptote of the function?

a)

x = 5

b)

x = 0

c)

x =5 , x = -5

d)

x = 25

5.

What's the vertical asymptote of the function?

a)

x = -4, x = 1

b)

x = 4, x = -1

c)

x = -4, x = -1

d)

x = 4, x = 1

6.

What is the equation of the graph?

a)
b)
c)
d)
7.

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)

8.

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

9.

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

a)

(1, 0)

b)

(-1, 0)

c)

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

d)

(0, 0), (1, 0)

10.
What is the Vertical Asymptotes?
a)
x= -4
b)
x= -4,5
c)
x= -5,5
d)
x= 4
11.
A vertical asymptote is found by setting the _________= to zero and solving for x 
a)
Numerator
b)
Denominator
c)
Right side 
d)
Left side
12.

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

13.

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

14.

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

15.

How do you know if a factor in the denominator is a hole instead of a V.A. ?

a)

It cancels out

b)

it equals 0

c)

you set the numerator equal to 0

d)

you compare the degrees

16.

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

a)

y = 0

b)

Slant Asymptote

c)

y =a / b

d)

What's an H.A.?

17.

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 =a / b

d)

What's an H.A.?

18.

Graph the function.

f(x)=x+1x4f\left(x\right)=\frac{-x+1}{x-4}  

a)
b)
c)
d)
19.

What (if any) holes exist?

a)

x=2

b)

x=2 and x=3

c)

x=-3

d)

x=3

20.

Find the coordinates of the hole.

a)

(-3, -3)

b)

(-3, 3)

c)

(3, -3)

d)

(3, 3)

21.

What is the slant (Oblique) asymptote for the equation

f(x) = (x2 - 4x + 2)/(x + 3)

a)

y = x -1

b)

y = x -7

c)

y = -7x + 23

d)

y = -2x + 2

22.

What type(s) of asymptotes does this function have? (Check all that apply.)

a)

Vertical

b)

Horizontal

c)

Slant

23.

What type(s) of asymptotes does this function have? (Check all that apply.)

a)

Vertical

b)

Horizontal

c)

slant