## Precalculus Practice Exam

Part 4 Test 3 Time: 2 hours

1. Given the equation, find the following:

• Amplitude,
• Period,
• Horizontal Shift (phase shift),
• Vertical Shift,
• Domain,
• Range,
• and four points that have a y-coordinate of 0.

2. Given that the point is located on the terminal side of the angle t, find a point on the terminal side of the following angles:
• -t

3. Write as an algebraic expression in x.

• Convert 128.3842 radians to degree measure in the format.

• The graph of is bounded by what two functions?
• Why are these two lines considered boundary functions?
• Graph the function and the two boundary functions.

4. A man, standing on the top of a building that is 1,000 feet high, looks down with an angle of depression of 12 degrees, to the base of the building across the street. How far apart are the buildings?

• Restrict the domain of the function to an interval where the function is increasing, and,
• Determine over that interval.
• Then sketch the graphs of both f and on the same coordinate system.
• What relationship do the graphs of these two functions have to the graph of the function g(x)=x?

5. A total of \$10,000 is invested for 10 years at 12% per year compounded continuously. How much interest will be earned during the 10 years?

6. Solve for x in the inequality

• When does .
• When does .
7. Assume that the population of a town in Texas is given by , where t time is given in years and t=0 corresponds to the year 1900.
• In what year was the population 60,000?
• Did the population ever reach 1,000,000?
• How long will it take for the population to reach 10,000?

8. Find all the zeros of .
• algebraically.
• graphically - explain how you interpreted the graph to arrive at your answer.

9. Solve the following system of equations for , and z: