Algebra 2 Rational Functions Test – Free PDF

Contents

This algebra 2 rational functions test checks rational functions and their graphs in 45 minutes, with 8 questions for a total of 20 points.

This test covers domain, asymptotes, holes, graphing and inverse variation for rational functions. It has eight questions worth 20 points in total. Show your work, write answers in simplest form, and use a straightedge for dashed asymptotes. Calculators are optional.

Test information

Grade: Algebra 2
Chapter: Rational Functions and Their Graphs
Common Core: F-IF.C.7d, F-IF.B.4
Time: 45 minutes
Total: 20 points (Question 1: 2 pts; Question 2: 3 pts; Question 3: 3 pts; Question 4: 2 pts; Question 5: 3 pts; Question 6: 2 pts; Question 7: 3 pts; Question 8: 2 pts)

Algebra 2 Rational Functions Test: questions 1–5

Question 1: Domain and asymptotes (2 points)

Let $f(x)=\frac{2x+1}{x-4}$.

State the domain and the vertical asymptote. (1 point)
State the horizontal asymptote. (1 point)

Question 2: Hole and asymptotes (3 points)

Let $f(x)=\frac{x^{2}-x-12}{x^{2}-9}$. Find the coordinates of the hole, the equation of the vertical asymptote, and the equation of the horizontal asymptote.

Question 3: Graph a rational function (3 points)

Graph $y=\frac{3}{x+2}-1$. Draw the asymptotes as dashed lines and plot at least four points.

Blank grid.

Question 4: Equation from a graph (2 points)

Write an equation of the form $y=\frac{a}{x-h}+k$ for the graph.

Dashed lines are the asymptotes.

Question 5: Inverse variation (3 points)

The variable $y$ varies inversely with $x$, and $y=9$ when $x=4$.

Write an equation relating $x$ and $y$. (1 point)
Find $y$ when $x=12$. (1 point)
Find $x$ when $y=2.25$. (1 point)

Algebra 2 Rational Functions Test: questions 6–8

Question 6: Graph with a hole (2 points)

The graph of $f(x)=\frac{x^{2}-4}{x+2}$ is shown.

A line with one open circle.

Give the coordinates of the open circle. (1 point)
State the domain of $f$. (1 point)

Question 7: Driving time (3 points)

Sofia drives 180 miles. The time is $t=\frac{180}{r}$ hours at an average speed of $r$ miles per hour.

Find the time at 45 mph. (1 point)
Find the speed that gives a time of 2.5 hours. (1 point)
Describe what happens to $t$ as $r$ gets very large, and name the horizontal asymptote. (1 point)

Question 8: Average cost (2 points)

Liam prints T-shirts. The setup costs $120 and each shirt costs $4 to print. The average cost per shirt for $n$ shirts is $C(n)=\frac{4n+120}{n}$ dollars.