How do you describe the end behavior of #f(x)=x^5-4x^3+5x+2#?

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Answer 1 · 2017-11-08T22:26:38

See below.

For end behaviour of a polynomial we only need to be concerned with the degree and leading coefficient as we approach #oo# and #-oo#

For this example the degree is 5 and leading coefficient is 1.

as #x-> oo# , #x^5-> oo#

as #x-> -oo# , #x^5-> -oo#

(a negative value raised to an odd power is always negative )

So range of function is:

#[y in RR }#

Graph: graph{x^5-4x^3+5x+2 [-14.24, 14.24, -7.12, 7.13]}