## Precalculus Test Out Practice Exam

Part 2 Test 3 Time: 3 hours

1. Find a rational function with vertical asymptotes at and a horizontal asymptote at y=3.

2. Find the slant asymptote to .

3. Find the equation of a polynomial with zeros x=3 and x=3+2i.

4. Find all the real zeros of the polynomial . What is the largest rational zero?

5. Divide by . What is the quotient?

6. Multiple and write the result in standard form: (10-8i)(2-3i).

7. The path of a ball is given by

where y is the height in feet and x is the horizontal distance in feet. Find the maximum height of the ball.

Answer: b) 50 feet.

8. Find the exact vertex of the parabola .

9. Find the constant in the equation of the parabola with vertex (3,4) with point (1,8).

10. What is the difference between the graphs of f(x) and

Answer: a) The graph of g(x) is the graph of f(x) shifted to the right 4 units, and up 3 units.

11. What is the remainder when you divide

by x-4 using synthetic division?

12. Find the upper bound of the zeros of using synthetic division.

13. Simplify and write in standard form a+bi: . Find the value of a.

14. How many real solutions does have?

15. Find the domain of the function .

Answer: c) All real numbers except .

16. Find the horizontal asymptote of the function .

17. Find the vertical asymptote to the right of the x-axis of the function .

18. Without using a calculator, approximate the value of at x=10,000,000,000.

19. Let x be the amount (in hundredths of dollars) a company spends on advertising, and let P be the profit, where . How much advertising will yield a maximum profit?

Answer: b) \$ 2,000.

20. Given , find .

21. Is a circle a function?

22. Is a parabola a one-to-one function?

23. The formula represents the volume of a cone. Find x in terms of the other variables.

24. Factor . What is the sum of the factors?

25. On what interval(s) is the function decreasing?