How do you describe the end behavior of #f(x)=-1/x^3+2#?

1 Answer
Dec 17, 2016

Answer:

As #x->+-oo#, #f(x)->2#

Explanation:

The end behavior of a function is the behavior of the graph of the function #f(x)# as #x# approaches #+oo# (positive infinity) or #-oo# (negative infinity).

As here #f(x)=-1/x^3+2#, as #x->oo#, #-1/x^3->0# and #f(x)->0+2=2#

and as #x->-oo#, #-1/x^3->0# and #f(x)->0+2=2#

In between as #x->0#, #f(x)->oo# when #x# approaches #0# from positive side and #f(x)->-oo# when #x# approaches #0# from negative side.
graph{-1/x^3+2 [-9.79, 10.21, -2.12, 7.88]}