# How do you graph y=-5/x using asymptotes, intercepts, end behavior?

Jul 9, 2018

#### Explanation:

Given: $y = - \frac{5}{x}$

This is called a rational function: $\frac{N \left(x\right)}{D \left(x\right)}$.

Find vertical asymptote(s):

When $D \left(x\right) = 0$ we have vertical asymptotes:

vertical asymptote at $x = 0$

End conditions:
The negative coefficient means the graph is reflected about the $x$-axis. So instead of starting in above the $x$-axis, the function starts below the $x$-axis.

Find y-intercept by setting $x = 0 :$

$y = - \frac{5}{0} \implies y =$undefined. $\text{ no } y$-intercept

Find x-intercepts by setting $y = 0 : \text{ } 0 = - \frac{5}{x}$

Multiply both sides by $x : \text{ "0 * x = -5, " } 0 = - 5$ Not TRUE

This means there is no $x$-intercepts.

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