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

1 Answer
Dec 8, 2017

Answer:

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:

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