Question

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

Answer 1

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`.