Question

What is the end behavior of `f(x) = x^6 + 2`?

Answer 1

The end behavior for `x^6+2` 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 up

The is the case because the degree of the function is even (6) which means it will go in the same direction to the left and right.

We know that it will go up because the leading co-efficient is positive (in this case the leading co-efficient is 1, as in `1x^6`).

Here's the graph of this function:

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