Question

Find Horizontal and Vertical asymptotes for y=(x^2 -9)/(4x^2 +1)

Answer 1

Answer: Horizontal asymptote is
`(1)/(4)` and vertical asymptotes are
`\pm (1)/(2i)`

Explanation:

Since we have given that

`y=(x^2-9)/(4x^2+1)`

We need to find the horizontal and vertical asymptotes.

Since vertical asymptotes will occur where the denominator becomes zero.

So, here denominator is
`4x^2+1`

Now,

`4x^2+1=0\\\\4x^2=-1\\\\x^2=(-1)/(4)\\\\x=\pm (1)/(2i)`

And the horizontal asympototes will occur when the coefficient of higher degree of numerator is divided by coefficient of higher degree of denominator.

`y=(1)/(4)`

Hence, horizontal asymptote is
`(1)/(4)` and vertical asymptotes are
`\pm (1)/(2i)`