Question

# Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. $f(x)=\frac{x-4}{5-x}$

Solution

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Step 1
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Degree of the numerator is equal to the denominator

The asymptote is set by the leading terms of each polynomial

Divide the leading coefficient of the top polynomial by the leading coefficient of the bottom polynomial.

$\dfrac{1}{-1}=-1$

The equation of the Horizontal Asymptote is $y=-1$

To find the Vertical Asymptote make sure the rational expression is in lowest terms

Whenever the polynomial of the denominator is equal to zero (any of its roots) we get a vertical asymptote.

$5-x=0$

$x=5$

The equation of vertical asymptote is $x=5$

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