How do you determine the end behavior of #f(x)=1/3x^3+5x#?

1 Answer
Feb 17, 2017

Answer:

#-oo# to the left and #oo# to the right

Explanation:

to know the end behavior of a function you need to know two things:
#1.# if the function is positive or negative
#2.# what the base function is, and what the base function looks like

#f(x)=1/3x^3+5x#
#1.# the function is positive, so it will be increasing
#2.#the base function is #y=x^3#

#graph: y=x^3#
graph{y=x^3 [-10, 10, -5, 5]}
so knowing that #f(x)=1/3x^3+5x# is positive and base function is #y=x^3#, it will be heading towards #-oo# to the left and #oo# to the right

the #1/3# and #5x# just makes the function become a really thin #y=x^3#

#graph:y=1/3 x^3 + 5x# (if you scroll out you'll see it better)
graph{y=1/3 x^3 + 5x [-10, 10, -5, 5]}