Algebra 2 Rational Functions Quiz – Free PDF

Contents

This algebra 2 rational functions quiz asks 10 multiple-choice questions on rational functions and their graphs, and each answer comes with a short explanation.

Ten multiple-choice questions check your skill with rational functions: asymptotes, domain and range, holes, graph transformations of y = 1/x, and inverse variation. Choose the one correct answer, then read the explanation to learn the typical mistake.

Algebra 2Common Core: F-IF.C.7d · F-IF.B.4

🎯 Rational Functions and Their Graphs – Algebra 2 math quiz

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Question 1

What is the vertical asymptote of $y=\frac{5}{x+7}-2$?

A $x=7$

B $x=-2$

C $x=2$

D $x=-7$

Question 2

What is the horizontal asymptote of $y=\frac{6x^{2}+1}{2x^{2}-5}$?

A $y=0$

B $y=6$

C $y=-\frac{1}{5}$

D $y=3$

Question 3

Which equation matches the graph?

A hyperbola with dashed asymptotes.

A $y=\frac{2}{x+2}-1$

B $y=\frac{2}{x-2}-1$

C $y=\frac{2}{x-2}+1$

D $y=-\frac{2}{x-2}-1$

Question 4

What is the domain of $f(x)=\frac{x+3}{x^{2}-16}$?

A $x\neq 4$

B $x\neq -3$

C $x\neq 16\text{ and }x\neq -16$

D $x\neq 4\text{ and }x\neq -4$

Question 5

How is the graph of $y=\frac{1}{x-4}+3$ related to the graph of $y=\frac{1}{x}$?

A Left 4 and up 3

B Right 4 and down 3

C Right 4 and up 3

D Right 3 and up 4

Question 6

The variable $y$ varies inversely with $x$, and $y=6$ when $x=4$. What is $y$ when $x=8$?

A $12$

B $48$

C $3$

D $24$

Question 7

The table shows an inverse variation. What is the constant $k$?

Values of an inverse variation.

A $36$

B $20$

C $9$

D $18$

Question 8

What is the range of $y=\frac{1}{x+3}+4$?

A $y\neq -4$

B $y\neq 3$

C $y\neq 4$

D $y\neq -3$

Question 9

The graph of $f(x)=\frac{x^{2}-9}{x-3}$ is shown. What are the coordinates of the open circle?

A line with one open circle.

A $(3,6)$

B $(3,0)$

C $(-3,0)$

D $(6,3)$

Question 10

A $240 bus rental is split equally among $n$ students, so each pays $c=\frac{240}{n}$ dollars. As $n$ gets very large, what happens to $c$?

A It becomes exactly $0

B It gets close to $0 but never equals $0

C It approaches $240

D It grows without bound

🎉 Quiz complete!

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How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Standards F-IF.C.7d and F-IF.B.4: graph rational functions and identify asymptotes, intercepts, domain and end behavior.
The graph of $y=\frac{a}{x-h}+k$ has asymptotes $x=h$ and $y=k$ and center $(h,k)$.
A canceled factor $x-c$ leaves a hole at $x=c$; a factor that remains in the denominator gives a vertical asymptote.
Compare degrees: smaller numerator gives $y=0$, equal degrees give the ratio of leading coefficients, larger numerator gives none.
Inverse variation $y=\frac{k}{x}$ means the product $xy$ is constant.