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Answered

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

Sagot :

First we need to check where the function gets undefined.

  • It's if denominator is 0

So solve it now

[tex]\\ \tt\hookrightarrow -3x^2+3x+18=0[/tex]

[tex]\\ \tt\hookrightarrow -3(x^2-x-6)=0[/tex]

[tex]\\ \tt\hookrightarrow x^2-x-6=0[/tex]

[tex]\\ \tt\hookrightarrow x^2+2x-3x+6=0[/tex]

[tex]\\ \tt\hookrightarrow x(x+2)-3(x+2)=0[/tex]

[tex]\\ \tt\hookrightarrow (x-3)(x+2)=0[/tex]

[tex]\\ \tt\hookrightarrow x=3\;or\:x=-2[/tex]

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