How do I find the asymptotes of #f(x)= (- 4x-x^2)/(2 + x^2)#?

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Answer 1 · 2018-05-05T06:04:15

Below

There is no vertical or oblique asmpytote. However, there is a horizontal asymptote

To find the horizontal asymptote, you have:

#lim _(x->0) (-4x-x^2)/(2+x^2)#

#lim_(x->0) (-4/x-1)/(2/x^2+1)#

#lim_(x->0) (-0-1)/(0+1)#

#lim_(x->0) -1#

#y=-1# is your horizontal asmyptote

graph{(-4x-x^2)/(2+x^2) [-10, 10, -5, 5]}

Looking at the graph, you can tell that it is approaching #y=-1# from both ends of the graph