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

Dec 19, 2017

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 $0$:

$x \left(x + 2\right) = 0$
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.

Hope this helps!