Question

How do you find the asymptotes for `f(x) = (x+1) / (x^2 +3x - 4)`?

Answer 1

`x=-4` and `x=+1`

Explanation:

Vertical asymptotes
substitute values of x that will make the denominator 0.
to do that you must factor, the denominator to obtain
`color(white)("XX") (x+4)(x-1)`,
then the values that would make this denominator 0 are
`color(white)("XX") -4 and +1`.

therefore, the equations of the asymptotes are,
`color(white)("XX") x=-4 and x=1`.
graph{(x+1)/(x^2+3x-4) [-6.244, 6.243, -3.12, 3.123]}

Note there are no horizontal asymptotes.