Question

How do you find the vertical, horizontal or slant asymptotes for `y = (4 x + 6)/(x - 1)`?

Answer 1

We have a vertical asymptote at `x=1` and horizontal asymptote at `y=4`.

Explanation:

As `x-1->0` i.e. `x->1`, `y->oo` and hence, we have a vertical asymptote given by `x=1`.

Further, we have `y=(4x+6)/(x-1)` and dividing numerator and denominator on right hand side by `x`, we get

`y=(4+6/x)/(1-1/x)`

and hence, as `x->oo`, `y->4/1=4` i.e. we have a horizontal asymptote `y=4`.

graph{(4x+6)/(x-1)[-20,20,-10,10]}