How do you find the asymptotes for #F(x) = (-2x^2 + 1)/(2x^3 + 4x^2)#?

1 Answer
A. S. Adikesavan
Dec 8, 2016

Vertical: #x=0uarr and uarrx=-2darr#. Horizontal:#larry=0rarr#.
For visual effect, see the graph.

Explanation:

#yto oo#, as #x to 0. yto +_oo#, as #x to -2#.

The line y=0, besides making x-intercepts #+-1/sqrt2#, is asymptotic

to two ( of the three ) branches of the graph, in the two opposite directions.

graph{2yx^2(x+2)+2x^2-1=0 [-10, 10, -5, 5]}

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