Precalculus I--Part 3--Test Out 1--With Answers.

Precalculus Test Out Practice Exam

Part 3 Test 1 Time: 3 hours

(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?

Answer: The point is (5,e+9).
When does

Answer: They are equal when x>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%.
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.

Answer: The equation is .
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.

Answer: The equation is .
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.
Find the exact solution for x in the equation

Answer: The exact solution is .
What is the domain of the function

Answer: The domain is the set .
Find the exact solution(s) to the equation

Answer: There is no solution because of domain restriction.
Write

as one term.

Answer: .
Find the exact value of

Answer: The exact value is 6.
Find the exact solution(s) to the equation

Answer: The exact solution is .
Find the exact solution(s) to the equation

Answer: The exact solution is x=6.
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.
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?

Answer: Approximately after 10 days.
Find the equation of the circle that passes through the points (2,1) (6,5) and (0,-5). Write the equation in standard form.

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

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

Answer: , y=22 and .
What is the maximum value of the function

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

Answer: .