What is the asymptotes of f(x)=(4x^2+1)/(2x^2-9) ?

The asymptotes of f(x)=(4x^2+1)/(2x^2-9) is Vertical: x=-3/(sqrt(2)),x= 3/(sqrt(2)),Horizontal: y=2

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asymptotes of f(x)=(4x^2+1)/(2x^2-9)

asymptotes

f (x) = \frac{4 x ^{2} + 1}{2 x ^{2} - 9}

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

Solution steps

Vertical asymptotes of

\frac{4 x ^{2} + 1}{2 x ^{2} - 9} : x = - \frac{3}{2}, x = \frac{3}{2}

Horizontal Asymptotes of

\frac{4 x ^{2} + 1}{2 x ^{2} - 9} : y = 2

Slant Asymptotes of

\frac{4 x ^{2} + 1}{2 x ^{2} - 9} :

None

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

- 4 x + 3

f (x) = 3 x + 2

e^{x}

x^{2} + 9

(3, 18), (3, 4)

What is the asymptotes of f(x)=(4x^2+1)/(2x^2-9) ?
The asymptotes of f(x)=(4x^2+1)/(2x^2-9) is Vertical: x=-3/(sqrt(2)),x= 3/(sqrt(2)),Horizontal: y=2