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TEST GRAPHING RATIONAL FUNCTIONS/ ALGEBRA 2 - Printable Mathematics Worksheets - Wayground

TEST GRAPHING RATIONAL FUNCTIONS/ ALGEBRA 2

20 questions

9th - 12th Grade

Mathematics

This free printable worksheet with an answer key helps Algebra II students in Grades 9–12 analyze and graph rational functions. Through 20 multiple-choice questions, students identify horizontal and vertical asymptotes, determine holes, simplify rational expressions, and find the domain and range of functions. Students also connect equations and graphs by writing rational-function equations from graphical features and selecting graphs that match given equations and asymptotes. The questions reinforce how numerator and denominator degrees determine horizontal asymptotes, how canceled factors create holes, and how denominator zeros relate to vertical asymptotes. Use it for guided practice, independent review, or an assessment of students’ ability to interpret key features of rational-function graphs.

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Worksheets

TEST GRAPHING RATIONAL FUNCTIONS/ ALGEBRA 2

Total questions: 20

Name
Class
Date
1.
What is the Horizontal Asymptote? 
a)
y= 5
b)
y= -6
c)
y= 1
d)
y= 5/-6
2.

The horizontal asymptote equals zero when:

a)

the degree of the numerator and denominator are equal

b)

the degree of the numerator is less than the degree of the denominator

c)

the degree of the numerator is greater than the degree of the denominator

d)

the numerator equals zero

3.

What (if any) holes exist?

a)

x=2

b)

x=2 and x=3

c)

x=-3

d)

x=3

4.
What is/are the vertical asymptote(s)?
a)
x=-2
b)
x=2 and x=3
c)
x=-3
d)
x=3
5.

Simplify the rational function

a)

1/(x + 5)

b)

1/(x - 5)

c)

(x - 5)(x + 5)

d)

(x - 5)/[(x - 5)(x + 5)]

6.
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
7.

What is the equation of the rational function graphed?

a)
b)
c)
d)
8.

What is the equation of the graph?

a)
b)
c)
d)
9.

Write an equation for the graph.

a)
b)
c)
d)
10.
a)
x=3
b)
x=1
c)
x=-3
d)
x=-2
11.
a)
x=1, x=-3
b)
x=-4
c)
x=1
d)
x=-4,x=-3
12.

Select the graph that show the corresponding vertical & horizontal asymptotes to this function

a)
b)
c)
d)
13.

Select the graph that show the corresponding vertical & horizontal asymptotes to this function

a)
b)
c)
d)
14.

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|

15.

What is the range of the function?

a)

 x=−1x=-1 

b)

 x≠−1x\ne-1 

c)

 y=−2y=-2 

d)

 y≠−2y\ne-2 

16.
Which asymptotes are determined by looking at the denominator of a function? 
a)
vertical
b)
horizontal
c)
slant
d)
none
17.

Which is the graph of the rational equation: y=1x+2−3y=\frac{1}{x+2}-3  

a)
b)
c)
d)
18.
A hole occurs when....
a)
You wear pants that are too tight.
b)
A factor from the numerator cancels with a factor in the denominator.
c)
The degree of the numerator is one more than the degree of the denominator.
d)
The denominator cannot be factored.
19.
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
20.
a)
All Reals Except 0
b)
All Reals
c)
All Reals Except -3
d)
All Reals Except 0 and -3
Answer Key

TEST GRAPHING RATIONAL FUNCTIONS/ ALGEBRA 2

Total questions: 20

1.
c) y= 1
2.
b)

the degree of the numerator is less than the degree of the denominator

3.
a)

x=2

4.
d) x=3
5.
a)

1/(x + 5)

6.
a) D : All real number x ≠ -3
R: All real number y≠ 1
7.
a)
8.
a)
9.
a)
10.
c) x=-3
11.
c) x=1
12.
b)
13.
a)
14.
c)

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

15.
d)

 y≠−2y\ne-2 

16.
a) vertical
17.
b)
18.
b) A factor from the numerator cancels with a factor in the denominator.
19.
b) x= 2, x=-2, y = 1
20.
c) All Reals Except -3

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FAQs

What does this rational functions worksheet cover?

This 20-question multiple-choice worksheet covers identifying horizontal and vertical asymptotes, locating holes, simplifying rational functions, and determining domain and range. Students also match equations to graphs and graphs to equations, building skill in connecting algebraic features with the visual behavior of rational functions.

How can I use this worksheet to teach graphing rational functions?

Use the questions in a sequence that starts with simplifying rational expressions and identifying canceled factors, then moves to holes, vertical asymptotes, horizontal asymptotes, domain, and range. Ask students to explain why a canceled factor produces a hole while a remaining denominator zero produces a vertical asymptote, and have them use those features to select or write the matching graph equation.

What mistakes should I watch for when students complete this rational functions worksheet?

Watch for students confusing a hole created by a canceled factor with a vertical asymptote, especially when selecting the x-value for each feature. Students may also reverse the degree rule for a horizontal asymptote, report a restricted x-value as part of the range, or choose a graph without checking both its vertical and horizontal asymptotes.

How do I assign and grade this rational functions worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for the 20 multiple-choice questions. Printable submissions can be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this rational functions worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the asymptote, hole, domain-and-range, and graph-matching choices are easier to read. You can also apply a dyslexia-friendly font or translate the rational-functions questions into another language.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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