How do you graph $f (x) = \frac{8}{x (x + 2)}$ $f(x)=8/(x(x+2))$ using holes, vertical and horizontal asymptotes, x and y intercepts?

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How do you graph $f (x) = \frac{8}{x (x + 2)}$ $f(x)=8/(x(x+2))$ using holes, vertical and horizontal asymptotes, x and y intercepts?

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Answer 1 · 2017-12-19T23:14:42

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 $0$ $0$ :

$x (x + 2) = 0$ $x(x+2) = 0$
vertical asymptotes: $x = 0, x = - 2$ $x = 0, x = -2$

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 $y = 0$ $y = 0$ .

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

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

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

Hope this helps!

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How do you graph $f (x) = \frac{8}{x (x + 2)}$ $f(x)=8/(x(x+2))$ using holes, vertical and horizontal asymptotes, x and y intercepts?

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

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How do you graph $f (x) = \frac{8}{x (x + 2)}$ $f(x)=8/(x(x+2))$ using holes, vertical and horizontal asymptotes, x and y intercepts?