Question

How to find the asymptotes of `f(x) = (x^2-1)/(2x^2 + 3x-2)`?

Answer 1

-2 and -1/2 are the asymptotes

Explanation:

To find the asymptotes of an equation, think of values that cannot be a result of the function when it is substituted by many values.

In this case, since it is a fraction, 0 denominator is not possible cpbecause it will lead to undefine , so to find the asymptotes, find values that could make the denominator.

So let `2x^2 + 3x -2=0`

Then solve for x

`2x^2 + 3x -2=0`
`(2x-1)(x+2)=0`
`2x-1=0`
`x=1/2`
And

`x+2=0`
`x=-2`

So the asymptotes are -2 and `1/2`