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The graph of $f(x)=\frac{2x}{x^2-5x-14}$ has vertical asymptotes $x=a$ and $x=b$, and horizontal asymptote $y=c$. Find $a+b+c$.

 Aug 29, 2017
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\( $f(x)=\frac{2x}{x^2-5x-14}$\)

 

Factoring the denominator, we have

 

2x / [ (x - 7)  ( x + 2) ]

 

Note that x = 7   or x  = -2   make the denominator undefined.....so these are the vertical asymptotes

 

And since the degree of the poynominal in the numerator is one less than that of the denominator, we will have a horizontal asymptote at y = 0

 

So.....the sum of the asymptotes  is  =  7 - 2 + 0   = 5

 

 

cool cool cool

 Aug 29, 2017
edited by CPhill  Aug 29, 2017

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