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]}