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    Contracting the Types of Asymptotes

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    I have been asked to explain and contract the types of asymptotes considered for rational functions. I have located the following but truly am having a difficulty understanding it. Thus, I have no idea what the below means unfortunately and I am therefore truly at a loss. Hopefully a better understanding of this will assist in helping me find a situation that fits an exponential function. As it is one step at a time.

    * Vertical asymptotes. These are vertical lines near which the function f(x) becomes infinite. If the denominator of a rational function has more factors of (x - a) than the numerator, then the rational function will have a vertical asymptote at x = a.

    * Horizontal Asymptotes. A horizontal asymptote is a line y = c such that the values of f(x) get increasingly close to the number c as x gets large in either the positive or negative direction. Rational functions have horizontal asymptotes when the degree of the numerator is the same as the degree of the denominator.

    * Oblique Asymptotes An oblique asymptote is an asymptote of the form y = a x + b with a non-zero. Rational functions have obliques asymptotes if the degree of the numerator is one more than the degree of the denominator. The function g(x) above has an oblique asymptote, namely the line y = x.

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    Solution Summary

    This explains the types of asymptotes and provides examples.