# How do you graph f(x)=8/x(x+2) using holes, vertical and horizontal asymptotes, x and y intercepts?

How do you graph $f\left(x\right)=\frac{8}{x\left(x+2\right)}$ using holes, vertical and horizontal asymptotes, x and y intercepts?
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Raven Mosley
holes: a value that causes both the numerator and denominator to equal zero. there are no holes in this rational function.

vertical asymptotes: it's a line $\to$ set the denominator of the rational function equal to 0:

x(x+2)=0
vertical asymptotes: x=0,x=−2

horizontal asymptotes:
the following are the rules for solving horizontal asymptotes:
let m be the degree of the numerator
let n be the degree of the denominator

if m > n, then there is no horizontal asymptote

if m = n, then the horizontal asymptote is dividing the coefficients of the numerator and denominator

if m < n, then the horizontal asymptote is y=0.

As we can see in our rational function, the denominator has a larger degree of x. So the horizontal asymptote is y=0.

x-ints: x-intercepts are the top of the rational function. Since the numerator just says 8, that means that there are no x-ints.

y-ints: y-intercepts are when you plug in 0 to the function:
$\frac{8}{0\left(0+2\right)}$
$\frac{8}{0}\to$ undefined, so there are no y-ints.