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

1 Answer
Somebody N.
Dec 8, 2017

See below.

Explanation:

Vertical asymptotes occur where the function is undefined.

-7/(x+4)−7x+4

For x=-4x=−4 -7/(x+4)=-7/(0)−7x+4=−70 undefined.

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

as x->oox→∞ , color(white)(888)-7/(x+4)->0888−7x+4→0

as x->-oox→−∞ , color(white)(888)-7/(x+4)->0888−7x+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:

enter image source here

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