What is the asymptotes of f(x)=(x^3-16x)/(3x^2+6x-9) ?

The asymptotes of f(x)=(x^3-16x)/(3x^2+6x-9) is Vertical: x=-3,x=1,Slant: y= 1/3 x-2/3

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asymptotes of f(x)=(x^3-16x)/(3x^2+6x-9)

asymptotes

f (x) = \frac{x ^{3} - 16 x}{3 x ^{2} + 6 x - 9}

Vertical : x = - 3, x = 1, Slant : y = \frac{1}{3} x - \frac{2}{3}

Solution steps

Vertical asymptotes of

\frac{x ^{3} - 16 x}{3 x ^{2} + 6 x - 9} : x = - 3, x = 1

Horizontal Asymptotes of

\frac{x ^{3} - 16 x}{3 x ^{2} + 6 x - 9} :

None

Slant Asymptotes of

\frac{x ^{3} - 16 x}{3 x ^{2} + 6 x - 9} : y = \frac{1}{3} x - \frac{2}{3}

Vertical : x = - 3, x = 1, Slant : y = \frac{1}{3} x - \frac{2}{3}

f (x) = \frac{1}{x ^{2} - 7 x + 10}

x + 3

f (x) = 2 x^{2} + 24 x + 76, - 6 \leq x \leq 2

- x - 2 - 3

f (x) = 2 x + 6

What is the asymptotes of f(x)=(x^3-16x)/(3x^2+6x-9) ?
The asymptotes of f(x)=(x^3-16x)/(3x^2+6x-9) is Vertical: x=-3,x=1,Slant: y= 1/3 x-2/3