AP®MathsCollege BoardPrecalculusExam QuestionsPolynomial & Rational FunctionsRational Functions

Rational Functions (College Board AP® Precalculus): Exam Questions

2 mins2 questions
1
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1 mark

In the x y-plane, the graph of a rational function f has a vertical asymptote at x = 3. Which of the following could be an expression for f \left(x\right) ?

  • \frac{\left(x - 3\right) \left(x + 1\right)}{2 \left(x + 3\right)}

  • \frac{\left(x + 2\right) \left(x - 3\right)}{\left(x - 1\right) \left(x - 3\right)}

  • \frac{\left(x - 3\right) \left(x + 4\right)}{\left(x + 3\right) \left(x - 1\right)}

  • \frac{\left(x + 3\right) \left(x + 1\right)}{\left(x + 1\right) \left(x - 3\right)}

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2
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1 mark

Let f be a rational function that is graphed in the x y-plane. Consider x = 2 and x = - 4. The polynomial in the numerator of f has a zero at x = 2 and does not have a zero at x = - 4. The polynomial in the denominator of f has zeros at both x = 2 and x = - 4. The multiplicities of the zeros at x = 2 in the numerator and in the denominator are equal. Which of the following statements is true?

  • The graph of f has holes at both x = 2 and x = - 4.

  • The graph of f has a vertical asymptote at x = 2 and a hole at x = - 4.

  • The graph of f has a hole at x = 2 and a vertical asymptote at x = - 4.

  • The graph of f has vertical asymptotes at both x = 2 and x = - 4.

Choose your answer