Question

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

Answer 1

The end behavior for `(x+3)^3` is the following:

• As x approaches positive infinity (far to the right) , the end behavior is up
• As x approaches negative infinity (far to the left), the end behavior is down

The is the case because the degree of the function is odd (3) which means it will go in opposite directions to the left and right.

We know that it will go up to the right and down to the left because the leading co-efficient is positive (in this case the leading co-efficient is 1).

Here's the graph of this function:

To learn more, read this answer:
How can you determine the end behavior of a function?