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

1 Answer
Feb 9, 2017

Answer:

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]}