## Precalculus Practice Exam

Part 4 Test 2 Time: 2 hours

1. Given the equation, find the following:

• Amplitude,

• Period,

• Horizontal Shift (phase shift),

• Vertical Shift,

• Domain,

Answer: The domain is , the set of all real numbers.

• Range,

Answer: The range is all values of y between -8 and -12.

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

Answer: Here are four such values of x that have a y-coordinate of -11:

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 172.3346 radians to degree measure in the format.

• The graph of is bounded by what two lines?

Answer: It is bounded by the lines y=3x-1, and y=3x+1.

• Why are these two lines considered boundary lines?

Answer: Because the biggest value can attain is 1, and the lowest value it can attain is -1, the graph of the function is caught between the two boundary lines 3x-1 and 3x+1.

• Graph the function and the two boundary lines.

4. A man, standing at the base of a building, looks up, with an angle of elevation of 42 degrees, to the top of the building across the street that is 2,000 feet high. How far apart are the buildings?

Answer: The two buildings are 2,221.22 feet apart.

• Restrict the domain of the function to an interval where the function is increasing.

Answer: The biggest interval which will be work is .

• 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 about the line g(x).

5. A total of \$40,000 is invested for 10 years at 14% per year compounded weekly. How much interest will be earned during the 10 years?

Answer: The interested earned after 10 years will be \$121,903.13.

6. Solve for x in the inequality

Answer: The set of solutions consists of all numbers x satisfying , 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: It will take approx. 12 years and 10 months, or 12.84 years.

• To triple?

Answer: It will take approx. 20 years and 4 months, or 20.345 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 rational zeros of .

Answer: The only rational solution for the equation f(x) is 1.

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