How do you graph f(x)=(x^3-16x)/(-3x^2+3x+18) using holes, vertical and horizontal asymptotes, x and y intercepts?

1 Answer
Feb 16, 2018

Factoring Steps:

f(x)=(x^3-16x)/(-3x^2+3x+18)

f(x)=((x)(x^2-16))/(-3(x-3)(x+2))

f(x)=((x)(x-4)(x-4))/(-3(x-3)(x+2))

Analysis of the rational equation:

There are no holes, because none of the terms cancel each other out in the numerator/denominator.

There are x intercepts at x=0,4,-4.

There are vertical asymptotes at x=-2, and 3.

because there is an x-intercept at x=0, that means that the t-intercept is also 0.

Therefore, the graph would look like this:

graph{(x^3-16x)/(-3x^2+3x+18) [-10, 10, -5, 5]}