4.7E: Rational Functions (Exercises)
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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. \(f(x)=\frac{2 x^{3}-x^{2}+4}{x^{2}+1}\)