# Write the function with a hole at x = 4 , a horizontal asymptote at y = 2 , and a vertical...

## Question:

Write the function with a hole at {eq}x=4 {/eq}, a horizontal asymptote at {eq}y=2 {/eq}, and a vertical asymptote at {eq}x=-1 {/eq}

## Graph of a Rational Function:

The rational function has a hole whenever the numerator and the denominator both evaluate to zero. It has a vertical asymptote where the denominator evaluates to zero but not the numerator. It has a horizontal asymptote when the degrees of the numerator and the denominator are the same.

First note that we are given that there is a hole at x=4, so the numerator and the denominator must evaluate to zero there. So we give a factor of x-4 ...

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