# How do you graph y=15/(x^2+2) using asymptotes, intercepts, end behavior?

Jan 15, 2018

See below.

#### Explanation:

$f \left(x\right) = \frac{15}{{x}^{2} + 2}$

Vertical asymptotes occur where the function is undefined.i.e.

${x}^{2} + 2 = 0$

There are no real solutions to this, so no vertical asymptotes.

As $x \to - \infty$ , $\textcolor{w h i t e}{888} \frac{15}{{x}^{2} + 2} \to 0$

As $x \to \infty$ , $\textcolor{w h i t e}{88888} \frac{15}{{x}^{2} + 2} \to 0$

${x}^{2} > 0$ for all $x \in \mathbb{R}$

So, x axis is a horizontal asymptote.

( This is also the end behaviour ).

Maximum value occurs when:

${x}^{2} + 2$ is at its minimum.

This is when $x = 0$

$y = \frac{15}{{\left(0\right)}^{2} + 2} = \frac{15}{2}$

GRAPH:

graph{15/(x^2+2) [-18.02, 18.01, -9.01, 9]}