Identify the vertical asymptotes of (x^3-16x)/(-3x^2+3x+18) Then sketch the graph.

asked Jan 13, 2023 183k views

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Identify the vertical asymptotes of
(x^3-16x)/(-3x^2+3x+18)

Then sketch the graph.

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First we need to check where the function gets undefined.

So solve it now

$\\ \tt\hookrightarrow -3x^2+3x+18=0$

$\\ \tt\hookrightarrow -3(x^2-x-6)=0$

$\\ \tt\hookrightarrow x^2-x-6=0$

$\\ \tt\hookrightarrow x^2+2x-3x+6=0$

$\\ \tt\hookrightarrow x(x+2)-3(x+2)=0$

$\\ \tt\hookrightarrow (x-3)(x+2)=0$

$\\ \tt\hookrightarrow x=3\;or\:x=-2$

Chinskiy answered Jan 17, 2023

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