## Precalculus Practice Exam

Part 2 Test 3 Time: 1 hour

1. The height of a projectile shot vertically upward from the ground with an initial velocity of 128 feet per second is given by the formula where t equals the time in seconds and h(t) equals the height above the ground at time t. What is the maximum height attained by the projectile?

Answer: The maximum height attained by the projectile is 256 ft.

2. Find a polynomial function with real coefficients that has 3 and 1+i as zeros.

3. Solve the following inequality for x:

Answer: The solutions for x are contained in the intervals .

4. Find all the real zeros of the polynomial

Answer: The solutions are: x=1, x=2, and .

5. Given the function where a, b, c, d, e and f are integers and a>0,

• Determine the right-hand and left-hand behavior of the graph of f(x).

Answer: The graph of f(x) approaches on the left and on the right.

• If -5 and 5 are zeros of f(x), and if f(-2)=12, f(0)=-18,and f(2)=50, how many real zeros does the function f(x) have?

Answer: The function has at least four distinct real zeros. If counted according to multiplicity, the function has five real roots (x=5 might be a double root).

6. Find all vertical and horizontal asymptotes for the graph of the following function and graph the function.

Answer: The horizontal asymptote is y=0, and the vertical asymptotes are x=6, and x=0.

7. Find the partial fraction decomposition for

8. Find the quadratic function whose graph has its vertex at (-1,8) and passes through the point (1,-4).

9. Sketch the graph of , showing clearly all x-intercepts and y-intercepts.