## 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.

Answer: The distance is .

• The midpoint of the two points.

Answer: The midpoint is (1,2).

• 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.

Answer:The relative maximum value is about 26.

• Approximate the relative minimum value of the function.

Answer:The relative minimum value is about -2.

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)?

Answer:The graph of -f(x) is reflected about the x-axis.

• 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 .

Answer: .

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Thu Jun 26 15:01:46 MDT 1997