How to find the asymptote of an exponential function?

Three types of asymptotes are possible with a rational expression. Horizontal asymptotes at the x-axis occur when the degree of the denominator is greater than the degree of the numerator. Horizontal axes occur at the ratio of the numerator and denominator's coefficients when the degrees of the numerator and denominator are the same. Vertical asymptotes occur where the denominator equals to zero. Slant asymptotes occur when the degree of the numerator is greater than the degree of the denominator.

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There are three types of asymptotes possible for any exponential function. Functions might have horizontal asymptotes, vertical asymptotes, and slant asymptotes. Any combination of these asymptotes occur in the case of rational expressions (functions which feature both a numerator and a denominator). The degree (i.e. the value of the exponent...

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There are three types of asymptotes possible for any exponential function. Functions might have horizontal asymptotes, vertical asymptotes, and slant asymptotes. Any combination of these asymptotes occur in the case of rational expressions (functions which feature both a numerator and a denominator). The degree (i.e. the value of the exponent attached to the variable) will determine what type of asymptote exists.

If the degree of the numerator is smaller than the degree of the denominator, the x-axis is a horizontal asymptote. This is also the case when, for example, there is a simple number (and no variable) in the numerator and a one-degree variable in the denominator ("1/x"). If the degree of the numerator is the same as the degree of the denominator, then the horizontal asymptote is a horizontal line whose y-value is the ratio of the coefficients of the numerator variable and the denominator variable. For example, y=3x/2x has a horizontal asymptote at y=3/2. Vertical asymptotes can be determined by setting the denominator equal to zero and finding the x-value that results in this.

The final scenario is when the degree of the numerator is greater than the degree of the denominator. In this case, there is a slant asymptote which can be determined by doing polynomial long division (an example of which appears at the link attached to this post).

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