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Algebra 2 · Chapter 4 · Lesson 4.11 · Printable PDF

Horizontal Asymptotes Worksheet with Answer Key

5 problems on horizontal asymptotes: finding them from degrees and leading coefficients, behavior far right and left when there is none, students' mistakes, writing a function with a given asymptote and crossing point, and finding constants from a graph. 2 pages, with a worked answer key.

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Printable Horizontal asymptotes worksheet with answer key - Algebra 2 (Page 1 PDF preview)
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Try one first: a free Chapter 1 worksheet (PDF, no sign-in).

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What's on the worksheet

  1. Find each horizontal asymptote, or say how the outputs behave far out.
    \dfrac{12x - 5}{4x + 9}\dfrac{x + 8}{x^2 - 3x + 1}\dfrac{7 - 8x^2}{x + 6x^2}\dfrac{(4 - x)(3x + 1)}{(2x - 5)(x + 6)}\dfrac{-2x^4 + x}{x^2 + 9}
  2. Find each student's mistake and give the correct statement.
  3. Write a rational function with a given asymptote that its graph crosses at exactly one input.
  4. Use two marked points to find the constants in the function whose graph is shown.
  5. Find the least denominator degree for a graph crossing its asymptote three times, and give an example.

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The free lesson teaches it with worked examples and practice problems.

Horizontal asymptotes: the lesson ›

More Chapter 4 worksheets: Rational expressions and rational functions