Question

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

Answer 1

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]}