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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.

52

Practice Questions

6

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 52.

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 another complex zero a - bi.
C) The function p(x) has no real zeros.
D) The function p(x) is a linear function.
E) The function p(x) has another complex zero bi - a
Show Answer

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

Q2MEDIUM

For the rational function f(x) = $\frac{x + 2}{$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 an oblique asymptote at y = x + 1
D) The function has a horizontal asymptote at y = 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) = $3x^{2}$ + 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) = $x^{2}$ - 4x + 3, find f(2)

A) -5
B) -1
C) 3
D) 1
E) -3
Show Answer

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

Q5MEDIUM

Find the roots of $x^{2}$ + 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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