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Graphing Rational Functions

Graphing Rational Functions 1.6 - Solution

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A rational function in the form y=axh+ky=\frac{a}{x-h}+k has a vertical asymptote at x=hx=h and a horizontal asymptote at y=k.y=k. Now we should find a function where h=-4h=\text{-}4 and y=7.y=7. Since hh is negative in the general formula we have to rewrite some of the expressions.

Function Rewrite Asympototes
A y=2x4+7y=\dfrac{2}{x-4}+7 x=4x=4 and y=7y=7
B y=2x47y=\dfrac{2}{x-4}-7 x=4x=4 and y=-7y=\text{-}7
C y=2x+4+7y=\dfrac{2}{x+4}+7 x=-4x=\text{-}4 and x=7x=7
D y=2x+47y=\dfrac{2}{x+4}-7 x=-4x=\text{-}4 and y=-7y=\text{-}7

Therefore, the correct option is C.