Question

Identify the vertical asymptotes of
`(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`