## Precalculus 2 Practice Exam

Test 1 Time: 1.5 hours

1. Find an equation for each asymptote of the graph of Answer: The graph has only one vertical asymptote, with equation . Note that the line x = -1 is not a vertical asymptote, since the numerator is also 0 at x = -1.

The equation for the oblique (slant) asymptote is . The graph has no horizontal asymptote.

2. Find all solutions for the equation 3. Find all solutions for the equation Answer: .

4. True or False?
• • • • 5. Suppose that in 1989 a species of turtle was accidentally released into a wetland. Four years later a biologist estimated that there were 300 turtles in the wetland. In 1996 she estimated that there were 450 turtles.

Let represent the size of the turtle population in the year t, where t=0 corresponds to the year 1989.

Find A, the initial population of turtles. And find r, the exponential growth rate.

Answer: The initial population A is 175. The exponential growth rate r is 0.135.

6. If the point (x,y)=(-3,-1) is on the terminal side of , give the exact values for:
• Answer: .

• Answer: .

• Answer: .

• Answer: .

7. If the terminal side of is in the third quadrant, and if , give exact values for:
• Answer: .

• Answer: .

• Answer: .

• Answer: .

8. Find all the angles between and that satisfy . Round your answers to three decimal places.

Answer: The angles are and .

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