# How do you graph #y=(x^3-8)/(6-x^2)# using asymptotes, intercepts, end behavior?

##### 1 Answer

Dec 21, 2016

#### Answer:

Slant asymptote:

#### Explanation:

By actual division.

horizontal asymptote y = quotient = -x and vertical asymptotes

The y-intercept is -4/3 and x-intercept is 2.

y' is 0 at

Local maximum ( for y'' < 0 ) at x = 3sqrt2, local minimum ( for y''>0 )

at x = -3sqrt2 and point of inflexion ( for y'' = 0 and y''' not 0 ) at x = 0.

Look at the graph that illustrates all these aspects.

graph{y(6-x^2)-x^3+8 =0 [-38.28, 38.28, -19.14, 19.14]}