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

Nov 21, 2015

As $x \rightarrow \infty , f \left(x\right) \rightarrow \infty$; as $x \rightarrow - \infty , f \left(x\right) \rightarrow - \infty$.

#### Explanation:

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

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

If you try negative numbers: $x = - 1000 , f \left(x\right) = - 999999999$.

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