Question

What is the end behavior of the graph of `y = 2x^3 + 5x`?

Answer 1

`As to +-oo, y to +-oo`.

Explanation:

`y > or <0` according as `x > or < 0`. The graph is in the first and third quadrants.

`y(-x)=-y(x)`. The graph is symmetrical about the origin.

It passes though the origin, at which `d/dx(y) = 5, d^2/dx^2(y)=0`.
Origin is a point of inflexion and, here, the tangent reverses its sense of rotation.

There is no asymptote.