Answer
$f(x)=\frac{2x^2}{x^2-4}$ matches the graph labeled (c)
Work Step by Step
The vertical asymptote is:
$x^2-4=0$
$x^2=4$
$x=\pm2$
The x-intercept:
$f(x)=\frac{2x^2}{x^2-4}=0$.
$x^2=0$
$x=0$
The graph passes through the origin.
The degree of the denominator is equal to the degree of the numerator. The horizontal asymptote is the ratio of the leading coefficients:
$y=\frac{2}{1}=2$
