## Precalculus Practice Exam

Part 4 Test 1 Time: 2 hours

1. Given the equation, find the following:

• Amplitude

• Period

• Horizontal Shift (phase shift)

• Vertical Shift

• Domain

Answer: , the set of all real numbers.

• Range

Answer: , or in interval notation: [5,11].

• and four points that have a y-coordinate of 11.

Answer: Here are four x-coordinates of such points:

Their y-coordinate is of course 11. There are other correct answers!

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 120.3346 radians to degree measure in the format.

• The graph of is bounded by what two lines?

Answer: It is bounded by the lines y=x+1 and y=x-1.

• Why are these two lines considered boundary lines?

Answer: Because the greatest value can be is 1, and the lowest value can be is -1. Thus the graph of the function is caught between the two boundary lines x-1 and x+1.

• Graph the function and the two boundary lines.

4. A man, standing on the top of a building that is 1,000 feet high, looks down, with an angle of depression of 42 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

Answer: The interval is the biggest interval which will work.

• 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?

Answer: The graph of is a reflection of the graph of f(x) over the line g(x).

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

Answer: The total interest earned is

6. Solve for x in the inequality

Answer: The set of solutions consists of all numbers x satisfying or x>-1, or in interval notation: .

7. Solve for x: . Explain how you checked your answer, step-by-step.

8. Assume that the world population at time t is given by
• How long will it take the world population to double?

Answer: approx. 15 years and 5 months, or 15.4 years

• To triple?

Answer: approx. 24 years and 5 months, or 24.41 years

• How long will it take for the population to decrease to one-half?

Answer: The population will never decrease as long as the same growth behavior continues.

9. Find the real zeros of given that 2i is a zero.

10. Solve the following system of equations for and z: