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Unit 4 of 5

Unit 4: Polynomial and Rational Functions

Study guide for CLEP CLEP College Algebra — Unit 4: Polynomial and Rational Functions. Practice questions, key concepts, and exam tips.

45

Practice Questions

24

Flashcards

6

Key Topics

Key Concepts to Study

polynomial division
rational roots theorem
asymptotes
holes
end behavior
partial fractions

Sample Practice Questions

Try these 5 questions from this unit. Sign up for full access to all 45.

Q1MEDIUM

What can be concluded about a polynomial function p(x) with real coefficients if it has a complex zero a + bi?

A.

The function p(x) must have a global maximum.

B.

The function p(x) has no real zeros.

C.

The function p(x) is a linear function.

D.

The function p(x) has another complex zero a - bi.

E.

The function p(x) has another complex zero bi - a

Show Answer

Answer: D — Complex zeros of polynomials with real coefficients come in conjugate pairs.

Q2MEDIUM

For the rational function f(x) = x+2x2−4\frac{x + 2}{x^2 - 4}, which of the following describes the characteristics of the function's end behavior?

A.

The function has a horizontal asymptote at y = 0

B.

The function has a vertical asymptote at x = 0

C.

The function has a horizontal asymptote at y = 1

D.

The function has an oblique asymptote at y = x + 1

E.

The function has a slant asymptote at y = x

Show Answer

Answer: A — The degree of the numerator is less than the degree of the denominator, so the horizontal asymptote is y = 0.

Q3MEDIUM

Find the equation of the axis of symmetry for the parabola f(x) = 3x23x^{2} + 2x - 1

A.

x = -2/3

B.

x = -1/3

C.

x = 1/3

D.

x = 1/2

E.

x = -1/6

Show Answer

Answer: B — x = -1/3 is correct because the axis of symmetry is x = -b/2a, and here a = 3, b = 2, so x = -1/3, not D which is the vertex's x-coordinate for a different parabola.

Q4EASY

If f(x) = x2x^{2} - 4x + 3, find f(2)

A.

-5

B.

-3

C.

-1

D.

1

E.

3

Show Answer

Answer: C — -1 is correct because f(2) = (2)^2 - 4(2) + 3 = -1.

Q5HARD

Find the roots of x2x^{2} + 2x + 2 = 0

A.

-1 + i

B.

1 - i and 1 + i

C.

1 + i

D.

-1 - i

E.

-1 + i and -1 - i

Show Answer

Answer: E — -1 + i and -1 - i is correct because use the quadratic formula to find complex roots -1 + i and -1 - i.

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Study Tips for Unit 4: Polynomial and Rational Functions

  • Focus on understanding concepts, not memorizing facts — CLEP tests application
  • Practice with timed questions to build exam-day speed
  • Review explanations for wrong answers — they reveal common misconceptions
  • Use flashcards for key terms, practice questions for deeper understanding

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