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

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Answer 1 · 2016-12-08T03:03:27

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

$yto oo$ , 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]}

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