## Precalculus Practice Exam

Part 3 Test 5 Time: 1 hour

• Explain why the graph of a rational function cannot cross its vertical asymptote.

Answer: It cannot cross its vertical asymptote because the graph would be undefined at that value of x.

• Where does the rational function

cross its horizontal asymptote?

Answer: It crosses its horizontal asymptote y=3 at x=-8/5.

• If

estimate the value of the function when x=20,000,000,000,000,000 using its oblique (slant) asymptote. Will this estimate be more or less than the actual value of the function at x=20,000,000,000,000,000? Why?

Answer: Using the slant asymptote y=2x+1, we obtain the estimate

which will be less than the actual value of of the function because to get the actual value the remainder is subtracted from the asymptote.

1. Let .

• Find .

• State the range and domain of and g(x).

Answer: The domain of g(x) is x>4, or in interval notation, .
The range of g(x) is all real numbers, or in interval notation, .

The domain of is all real numbers, or in interval notation, .
The range of is y>4, or in interval notation, .

• Sketch both functions on the same coordinate axis.

• For which values of x is ?

Answer: They are equal only when x>0.

• For which values of x is ?

Answer: They are equal only when x>0.

• For which values of x is ?

Answer: They are equal only when x=1, or .

• For which values of x is ?

Answer: They are equal only when x=1, or when .

3. Find all the solutions of the system

• Using the method of substitution,

• By sketching the graphs of both equations.

4. Suppose that \$9500 is invested at 7.6% interest compounded monthly. How long will it take for the amount in the account to reach \$20,000?

Answer: It will take approximately 9 years and 10 months, or 9.8 years.

If you would like to practice another Part 3 exam, click on Next Exam.

If you would like to practice on exams for Parts 1, 2 or 4, click on Menu. It will take you back to the original menu.

Tue Jul 1 16:42:23 MDT 1997