What is the end behavior of X^3-5x?

1 Answer
Mar 7, 2018

The end behavior of this function is:
as #x -> oo# , #y -> oo#
as #x -> -oo# , #y -> -oo#
because it is an odd, positive function.

Explanation:

graph{x^3-5x [-10, 10, -5, 5]}

You can also remember it like this:
(Function is odd/even based on the degree of function.
Function is positive/negative based on the the sign of the leading coefficient.)

odd positive function =
as #x -> oo# , #y -> oo#
as #x -> -oo# , #y -> -oo#

odd negative function=
as #x -> oo# , #y -> -oo#
as #x -> -oo# , #y -> oo#

even positive function =
as #x -> oo# , #y > oo#
as #x -> -oo# , #y -> oo#

even negative function=
as #x -> oo# , #y -> -oo#
as #x -> -oo# , #y -> -oo#