## Precalculus Test Out Practice Exam

Part 3 Test 1 Time: 3 hours

1. (1,e) is a point on the graph of . If the graph of f(x) is shifted so that it is superimposed on the graph of f(6-x)+9, where is the point (1,e) located after the shift?

2. When does

Answer: They are equal when x>3.

3. A total of \$1,000 is invested at 10%, compounded monthly for five years. What is the balance after five years? What is the effective rate?

Answer: The balance after 5 years is approximately \$1,645.31. The effective rate is 10.47%.

4. If you start an experiment with four cells that double every minute, write an equation with base e that describes the number of cells present at any time.

5. If you start an experiment with four cells that double every minute, write an equation with base 6 that describes the number of cells present at any time.

6. Find the inverse of the function . If the domain needs to be restricted to find the inverse state the restricted domain. If the domain does not need to be restricted to find the inverse, explain.

Answer: with domain: x>2. The domain of f does not need to be restricted since the function is already a one-to-one function.

7. Find the exact solution for x in the equation

Answer: The exact solution is .

8. What is the domain of the function

Answer: The domain is the set .

9. Find the exact solution(s) to the equation

Answer: There is no solution because of domain restriction.

10. Write

as one term.

11. Find the exact value of

Answer: The exact value is 6.

12. Find the exact solution(s) to the equation

Answer: The exact solution is .

13. Find the exact solution(s) to the equation

Answer: The exact solution is x=6.

14. Which balance is largest after five years?
• \$ 1,000 invested at 10 % compounded continuously.
• \$ 1,000 invested at 10.3 % compounded monthly.
• \$ 1,000 invested at 10.1 % compounded weekly

Answer: The largest balance is \$1,000 at 10.3% compounded monthly.

15. On a college campus of 5,000 students, one student returned from vacation with a contagious flu virus. The spread of the virus through the student body is given by

where y is the total number of students infected after t days. The college will cancel classes when 40% or more of the students are ill. After how many days will the college cancel classes?

16. Find the equation of the circle that passes through the points (2,1) (6,5) and (0,-5). Write the equation in standard form.

17. Write the equation of the parabola that passes through the points (2,9), (-2,29) and (1,5). Write the equation in standard form.

18. Solve the following set of equations for x, y and z:

19. What is the maximum value of the function

Answer: The maximum value is f(x)=39.

20. What is the equation of the line that passes through the points of intersection of the two circles

Write the equation of the line in the form ax+by+c=0, where the values a, b, and c are the exact values, not approximations.