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

 Feb 27, 2018
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In the rational function \(f(x)=\frac{2x}{x^2-5x-14}\), we can determine the vertical asymptotes by setting the denominator equal to 0 and solving for x. 

 

\(x^2-5x-14=0\) In this case, the left-hand-side quadratic is factorable, which eases the process of finding the zeros. 
\((x-7)(x+2)=0\) Use the zero product thereom to find the remaining zeros. 
\(x_1=a=7\\ x_2=b=-2\)  
   

 

The horizontal asymptote requires some observation. The horizontal asymptote lies on y=0 since the degree of the numerator is less than the degree of the denominator. Therefore, c=0. We know the unknown variables, so we can now calculate their collective sum.

 

\(a+b+c\\ 7-2+0\\ 5\)

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 Feb 27, 2018

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