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 ( x ) = x 3 - 16 x - 3 x 2 + 3 x + 18 using holes, vertical and horizontal asymptotes, x and y intercepts?
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Answers (1)

incibracy5x
Answered 2022-09-17 Author has 21 answers
f ( x ) = x 3 - 16 x - 3 x 2 + 3 x + 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]}

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