4.7E: Rational Functions (Exercises)

Algebra and Trigonometry · LibreTexts

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    For the following exercises, find the intercepts and the vertical and horizontal asymptotes, and then use them to sketch a graph of the function.

    31. \(f(x)=\frac{x+2}{x-5}\)

    32. \(f(x)=\frac{x^{2}+1}{x^{2}-4}\)

    33. \(f(x)=\frac{3 x^{2}-27}{x^{2}+x-2}\)

    34. \(f(x)=\frac{x+2}{x^{2}-9}\)

    For the following exercises, find the slant asymptote.

    35. \(f(x)=\frac{x^{2}-1}{x+2}\)

    36. \(f(x)=\frac{2 x^{3}-x^{2}+4}{x^{2}+1}\)

    This page titled 4.7E: Rational Functions (Exercises) was last modified on Tue, 08 Feb 2022 17:57:03 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.