## Precalculus Practice Exam

Part 1 Test 3 Time: 1 hour

1. Solve the following equation for x:

Answer: , and .

2. Solve the following inequality for x:

Answer: The set of values x<5.

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).

• An equation of the line containing the two points.

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

• An 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 always increasing, thus, the increasing interval is .

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

Answer: The function is never decreasing.

• Approximate the relative maximum value of the function.

Answer: Since the function is always increasing, there is no maximum value.

• Approximate the relative minimum value of the function.

Answer: There is no minimum value of the function.

5. Concerning the graph of f(x) in Problem 4, sketch the following:
• -f(x).
Answer:

• f(x)+3.
Answer:

• f(x-4)-6.
Answer:

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

Answer:

• Find .

Answer:

• Find .

Answer: f(g(x))=|x|-3.

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If you would like to practice on exams for Parts 2, 3 or 4, click on Menu . It will take you back to the original menu.

Tue Jun 24 15:37:09 MDT 1997

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