Examples: Find the horizontal asymptote of each rational function:First we must compare the degrees of the polynomials. Both the numerator and denominator are 2nd degree polynomials. Since they are the same degree, we must divide the coefficients of the highest terms. In the numerator, the ...
Next I'll turn to the issue of horizontal or slant asymptotes. Since the degrees of the numerator and the denominator are the same (each being 2), then this rational has a non-zero (that is, a non-x-axis) horizontal asymptote, and does not have a slant asymptote. The horizontal asymp...
An asymptote is a line that the graph of a function approaches but never touches. Rational functions contain asymptotes, as seen in this example: In this example, there is a vertical asymptote at x = 3 and a horizontal asymptote at y = 1. The curves approach these asymptotes but never cr...
Slant Asymptote Rules Vertical and horizontal asymptotes can occur in a variety of different types of functions. However, slant asymptotes most commonly appear for two types of functions. The first type of function is a rational function, of the form {eq}\frac{f(x)}{g(x)} {/eq}, where...
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