# How do you graph f(x)=-3/x using holes, vertical and horizontal asymptotes, x and y intercepts?

Jun 10, 2018

See graph

no holes.

#### Explanation:

Set $x = 0$ to solve for $y$ intercept:

$f \left(x\right) = - \frac{3}{x}$

$- \frac{3}{0}$ in undefined so no $y$ intercept exists

Set $f \left(x\right) = y = 0$ to solve for $x$ intercept(s):

$0 = - \frac{3}{x}$

$0 = - 3$ is not possible so no $x$ intercept(s) exist.

There are no holes because you cannot cancel any factors with $x$ in them from the denominator.

Set the denominator=0 to solve fo asymptotes:

$x = 0$ so there is a vertical asymptote at $y = 0$.

$x \to \pm \infty , f \left(x\right) \to 0$ so there is a horizontal asymptote at $x = 0$

graph{-3/x [-10, 10, -5, 5]}