## Precalculus Practice Exam

Part 4 Test 7 Time: 2 hours

• Express the angle in radians.

• Express 546.954 radians in format.

1. For the function , determine the:
• (h) amplitude,

• (i) period,

• vertical shift,

• phase shift,

• domain,

• range.

• Can f(t)=-2? Explain.

Answer: no because the range of f(t) goes is between 4 and 16, and since -2 is not in between those numbers, therefore f(t) can't never be -2.

2. Simplify each expression:
• .

• .

3. Given that and , find the remaining five trigonometric functions of the angle .

4. Find if . Restrict domain if necessary.

Answer: . The restricted domain is .

5. Find the inverse of the following function (restrict the domain if necessary):

• Restrict the domain to all .

• Answer: The domain is restricted to all x > 10 .

6. If you invested \$1,000 for 4 years as follows:
• Years 1 and 2 compounded weekly at 11%, and years 3 and 4 continuously at 13%.
• What simple interest rate would give you the same balance as the above after four years?

Answer: At the end of 2 years we will have approximately \$1245.79, and at the end of 4 years we will have approximately \$1615.69.

A simple interest rate of 12.74 % pear year will yield the same balance as the above after four years.

7. Find a polynomial function that passes through the point (3,24), has a double zero of 3 and zeros 1 and -1

• Of degree 3.

Answer: This is not possible. If 3 is a double zero, then we have 4 zeros above. The smallest degree of a polynomial having 1, -1 and double 3 as their zeros has to be 4 according to the fundamental theorem of algebra.

• Of degree 4.

• Of degree 6.

There are many possible solutions for this. However all the exponents of each of the terms must add up to 6.

8. Solve for x:

Answer: The domain is restricted to all x>1. By solving this equation algebraically we get two solutions, x=1 and x=6, but since x=1 is not in the domain of the original equation, then the only solution is x=6.

9. Find the quadratic function whose graph contains the points (1,-2),(2,1) and (-1,10).

10. Suppose you are given a polynomial function of degree four with a relative maximum of 10 located at x=0, a relative maximum of 22 located at x=10, and a relative maximum of -5 located at x=4. On what interval(s) is the function:

• Increasing?

Answer: The function is increasing on the intervals .

• Decreasing?

Answer: The function is decreasing on the intervals .

• Give two intervals where at least one of the zeros of the polynomial exists.

Answer: Two intervals are and .
There are several other solutions.

If you would like to practice on exams for Parts 1, 2 or 3, click on Menu. It will take you back to the original menu.

Fri, March 6, 1998