Question

How do you find the asymptotes for `y= (7x-2) /( x^2-3x-4)`?

Answer 1

The asymptotes of any expression are found by defining what happens to the expression when `x -> oo` or `x-> - oo` or when `y->oo`

Explanation:

The asymptotes of any expression are found by defining what happens to the expression when `x -> oo` or `x-> - oo` or when `y->oo`
In this case `y =(7x+2)/(x^2 - 3x - 4)` or `(7x-2)/((x-4)(x+1))`

Hence when `x ->4` or `x -> -1` then `y -> oo`. Therefore there are vertical asymptotes at `x =4` and at `x=-1`

`lim _( x-> +-oo) (7x-2)/(x^2-3x-4) = lim_(x->+-oo) 7/x =0`