## Precalculus Practice Exam

Part 1 Test 4 Time: 1 hour

1. Solve the following equation for x:

2. Solve the following inequality for x:

Answer:The values of x that make this inequality true are included on the intervals .

3. Given the two points (-1,8) and (3,-4), find the following:
• The distance between the two points.

• The midpoint of the two points.

• The equation of the line between the two points.

Answer:The equation of the line is y=-3x+5.

• The equation of the circle whose diameter is the line between the two points.

Answer: The circle is the locus of the points described by

4. Concerning the following graph of f(x),
• Approximate the interval(s) where the function is increasing.

Answer: The function is increasing approximately on the intervals

• Approximate the interval(s) where the function is decreasing.

Answer: The function is decreasing approximately on the interval .

• Approximate the relative maximum value of the function.

• Approximate the relative minimum value of the function.

5. Answer the following questions concerning the graph of f(x) in Problem 4:
• How does the graph of -f(x) differ from the graph of f(x)?

• How does the graph of f(x)+3 differ from the graph of f(x)?

Answer:The graph of f(x)+3 has a vertical shift of 3.

• How does the graph of f(x-4)-6 differ from the graph of f(x)?

Answer:The graph of f(x-4)-6 has a vertical shift of -6 and a horizontal shift of 4.

6. Given the functions and , find the following:
• Find (f+g)(x).

• Find .

• Find .