Question

How do you find the end behavior of `9x^5 - 8x^3 + 4x`?

Answer 1

See below.

Explanation:

The end behaviour of `9x^5 - 8x^3 + 4x` will be determined by the leading (dominant) term `9x^5`.

Ie for `abs x ">>" 0`, we have `y approx 9x^5`. The right and left ends of this graph (which is of `y = 9x^5`) will, therefore, show how the function operates as `x to pm oo`

graph{9x^5 [-3.796, 3.817, -1.905, 1.904]}

The full function looks like this:

graph{9x^5 - 8x^3 + 4x [-3.796, 3.817, -1.905, 1.904]}