Free CLEP Precalculus Practice Questions

Sample Practice Questions

Try these 10 sample questions from the CLEP Precalculus practice bank. Each includes the answer and explanation. Continue with the interactive practice above to review the full question set.

1. 1For a nonzero real number x, simplify the product x^3 · x^5.

   1. A.x^8Correct answer: A
   2. B.x^15
   3. C.2x^8
   4. D.x^2

   Explanation: OpenStax states, "Products of exponential expressions with the same base can be simplified by adding exponents." Adding 3 and 5 gives x^8.

   Reference: College Algebra 2e, Chapter 1 Key Concepts — 1.2 Exponents and Scientific Notation

2. 2Which of these relations assigns exactly one output to each input x?

   1. A.{(1, 2), (1, 3), (2, 4)}
   2. B.{(1, 2), (2, 3), (3, 2)}Correct answer: B
   3. C.{(1, 2), (2, 3), (2, 4)}
   4. D.{(1, 2), (3, 2), (3, 4)}

   Explanation: OpenStax states, "A function is a specific type of relation in which each domain value, or input, leads to exactly one range value, or output." In B each input occurs with exactly one output; repeated outputs are allowed.

   Reference: Precalculus 2e, Chapter 1 Key Concepts — 1.1 Functions and Function Notation

3. 3A new function subtracts four from every output of f: g(x) = f(x) − 4. How does its graph move?

   1. A.Shifted 4 units downCorrect answer: A
   2. B.Shifted 4 units up
   3. C.Shifted 4 units right
   4. D.Shifted 4 units left

   Explanation: OpenStax says, "The vertical shift results from a constant added to the output. Move the graph up for a positive constant and down for a negative constant." Subtracting 4 shifts each output down 4.

   Reference: Precalculus 2e, Section 1.5 Transformation of Functions — Graphing Functions Using Vertical and Horizontal Shifts

4. 4What is the x-intercept of the line y = 2x − 8?

   1. A.The point with x zero and y negative eight
   2. B.The point with x zero and y positive four
   3. C.The point with x positive four and y zeroCorrect answer: C
   4. D.The point with x negative four and y zero

   Explanation: OpenStax states, "The x-intercept is the point at which the graph of a linear function crosses the x-axis." Set y = 0: 2x − 8 = 0 gives (4, 0).

   Reference: Precalculus 2e, Chapter 2 Key Concepts — 2.2 Graphs of Linear Functions

5. 5An angle θ terminates in quadrant II. Which signs do sin θ and cos θ have?

   1. A.Both positive
   2. B.Sine positive, cosine negativeCorrect answer: B
   3. C.Sine negative, cosine positive
   4. D.Both negative

   Explanation: OpenStax states, "The signs of the sine and cosine are determined from the x- and y-values in the quadrant of the original angle." In quadrant II, y is positive and x is negative.

   Reference: Precalculus 2e, Chapter 5 Key Concepts — 5.2 Unit Circle: Sine and Cosine Functions

6. 6A rental service charges $15 plus $4 per hour. Which function gives the total cost C(h) for h hours?

   1. A.C(h) = 15h + 4
   2. B.C(h) = 4h + 15Correct answer: B
   3. C.C(h) = 19h
   4. D.C(h) = 15 − 4h

   Explanation: OpenStax states, "Linear models may be built by identifying or calculating the slope and using the y-intercept." The fixed charge is 15 and the hourly rate is 4.

   Reference: Precalculus 2e, Chapter 2 Key Concepts — 2.3 Modeling with Linear Functions

7. 7Divide the following powers, assuming that y is a nonzero real number: y^7 / y^4.

   1. A.y^11
   2. B.y^3Correct answer: B
   3. C.y^4
   4. D.1/y^3

   Explanation: OpenStax states, "Quotients of exponential expressions with the same base can be simplified by subtracting exponents." Subtracting 4 from 7 gives y^3.

   Reference: College Algebra 2e, Chapter 1 Key Concepts — 1.2 Exponents and Scientific Notation

8. 8If f(x) = 2x² − 3x, what is f(−2)?

   1. A.Positive two
   2. B.Negative two
   3. C.Positive fourteenCorrect answer: C
   4. D.Negative fourteen

   Explanation: OpenStax states, "Algebraic forms of a function can be evaluated by replacing the input variable with a given value." Substituting −2 gives 2(−2)² − 3(−2) = 14.

   Reference: Precalculus 2e, Chapter 1 Key Concepts — 1.1 Functions and Function Notation

9. 9Which transformation produces h(x) = f(x − 3) from the original graph of f?

   1. A.Shifted 3 units left
   2. B.Shifted 3 units rightCorrect answer: B
   3. C.Shifted 3 units down
   4. D.Shifted 3 units up

   Explanation: OpenStax says, "The horizontal shift results from a constant added to the input. Move the graph left for a positive constant and right for a negative constant." The input change is −3, so the graph moves right.

   Reference: Precalculus 2e, Section 1.5 Transformation of Functions — Graphing Functions Using Vertical and Horizontal Shifts

10. 10A nonvertical line has slope 2/3. What is the slope of a line perpendicular to it?

    1. A.Positive two thirds
    2. B.Negative two thirds
    3. C.Negative three halvesCorrect answer: C
    4. D.Positive three halves

    Explanation: OpenStax states, "Perpendicular lines have negative reciprocal slopes, assuming neither is vertical." The negative reciprocal of 2/3 is −3/2.

    Reference: Precalculus 2e, Chapter 2 Key Concepts — 2.2 Graphs of Linear Functions