## 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,
• (j) vertical shift,
• (k) phase shift,
• (l) domain,
• (m) range.
• (n) Can f(t)=-2? Explain.

2. Simplify each expression:
• .
• .

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

4. Find if . Restrict domain if necessary.

5. Find the inverse of the following function(restrict the domain if necessary):
6. If you invested \$1,000 for 4 years as follows:
• Years 1 and 2 compounded weekly at 11%,
• Years 3 and 4 continuously at 13%,
• What simple interest rate would give you 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.
• Of degree 4.
• Of degree 6.

8. Solve for x:

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