Rational Functions and Their Graphs: Algebra 2 Math Test – PDF Download

Question 1: Domain and asymptotes (2 points)

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

1. State the domain and the vertical asymptote. (1 point)
2. 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.

Question 4: Equation from a graph (2 points)

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

Question 5: Inverse variation (3 points)

The variable \(y\) varies inversely with \(x\), and \(y=9\) when \(x=4\).

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

Question 6: Graph with a hole (2 points)

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

1. Give the coordinates of the open circle. (1 point)
2. 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.

1. Find the time at 45 mph. (1 point)
2. Find the speed that gives a time of 2.5 hours. (1 point)
3. 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.

1. Find the average cost for 30 shirts. (1 point)
2. How many shirts give an average cost of $5? (1 point)

⬇ Download the Algebra 2 Rational Functions and Their Graphs test (PDF, 90 KB)

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