Algebra and Trigonometry 10th Edition

$f(x)=\frac{x^3}{4(x+2)^2}$ matches with the graph labeled (d).
The vertical asymptote is: $4(x+2)^2=0$ $(x+2)^2=0$ $x+2=0$ $x=-2$ The x-intercept: $f(x)=\frac{x^3}{4(x+2)^2}=0$. $x^3=0$ $x=0$ The graph passes through the origin. The degree of the numerator is greater than the degree of the denominator. The graph has no horizontal asymptotes.