Question

Identify the vertical asymptotes of $\frac{x^3-16x}{-3x^2+3x+18}$
Then sketch the graph.

Answer 1

First we need to check where the function gets undefined.

• It's if denominator is 0

So solve it now

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

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

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

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

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

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

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