 # How do you graph f(x)=(x^3−16x)/(−3x^2+3x+18) using holes, vertical and horizontal asymptotes, x and y intercepts? rustenig 2022-09-16 Answered
How do you graph $f\left(x\right)=\frac{{x}^{3}-16x}{-3{x}^{2}+3x+18}$ using holes, vertical and horizontal asymptotes, x and y intercepts?
You can still ask an expert for help

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it incibracy5x
$f\left(x\right)=\frac{{x}^{3}-16x}{-3{x}^{2}+3x+18}$
$f\left(x\right)=\frac{\left(x\right)\left({x}^{2}-16\right)}{-3\left(x-3\right)\left(x+2\right)}$
$f\left(x\right)=\frac{\left(x\right)\left(x-4\right)\left(x-4\right)}{-3\left(x-3\right)\left(x+2\right)}$
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]}

We have step-by-step solutions for your answer!