To find the asymptote of a rational function defined by a rational expression in lowest term, use the following procedure:
1). Vertical Asymptote
Find any vertical asymptotes by setting the denominator equal to zero and solving for y. If a is zero of the denominator, then the line y=a is a vertical asymptote.
2). Other Asymptotes
Determine any other asymptotes consider three possibilities:
a.) If the numerator has a lower degree than tge denominator, then there is a horizontal asymptote y=0
b.) If the numerator and denominator has the same degree.
c.) If the numerator is of degree exactly one more than the denominator then there will be an oblique(slanted) asymptote. To gind it, divide the numerator by tge denominator and disregard the remainder. Set the rest of the qoutient equal to y to obtain the equation of the asymptote.
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