What is the end behavior of #f(x) = x^3 + 1#?

1 Answer
Nov 21, 2015

Answer:

As #xrarroo,f(x)rarroo#; as #xrarr-oo,f(x)rarr-oo#.

Explanation:

A good way to test this is to plug in increasingly larger numbers in both the positive and negative directions.

For example, if #x=1000, f(x)=1000000001#. It is clear that #f(x)# will only keep increasing towards positive infinity if you plug in greater and greater positive numbers.

If you try negative numbers: #x=-1000, f(x)=-999999999#.

The negative number, when cubed, will always result in an negative number again. These numbers will get closer and closer to #-oo#.