Question

How do you find the vertical, horizontal or slant asymptotes for `-7 / (x+4)`?

Answer 1

See below.

Explanation:

Vertical asymptotes occur where the function is undefined.

`-7/(x+4)`

For `x=-4` `-7/(x+4)=-7/(0)` undefined.

The line `color(blue)(x=-4)` is a vertical asymptote:

as `x->oo` , `color(white)(888)-7/(x+4)->0`

as `x->-oo` , `color(white)(888)-7/(x+4)->0`

The x axis is a horizontal asymptote:

There is no oblique asymptote. Oblique asymptotes occur when the degree of the polynomial in the numerator is greater than the degree of the polynomial in the denominator.

Graph: