Question

Find the vertical asymptote(s) of f of x equals quantity 2 x squared plus 3x plus 6 end quantity over quantity x squared minus 1.

x = −1, 1
x = 1, 2
x = −1, 2
x = −2, 2

Answer 1

x = −1, 1

Explanation:

Answer 2

x = −1, 1

Explanation:

Vertical Asymptotes

A vertical asymptote of the graph of a given function f(x) is the line x=a, such that one of of these statements is fulfilled

`\displaystyle \lim _(x\to a^(+))f(x)=\pm \infty`

`\displaystyle \lim _(x\to a^(+))f(x)=\pm \infty`

If f(x) is a rational expression, we must find all the values of x who make the denominator equal to zero

`\displaystyle f(x)=(2x^2+3x+6)/(x^2-1)`

We set the denominator to zero

`x^2-1=0`

`(x-1)(x+1)=0`

`x=-1,\ x=1`

Those are the vertical asymptotes of f