Question

Which of the following could have the end behavior: as x goes to infinity f(x) goes to infinity, and as x goes to negative infinity f(x) goes to infinity?

ax

-ax^5+bx^2+cx

ax^6

ax^3 + bx^2 + c

ax^4 - bx^3 - cx^2 - dx +e

ax^2 - b

Answer 1

So multiple of the following could have the end behaviors described. Do you have the option to pick more than one?

Any of these: ax^6; ax^4 - bx^3 - cx^2 - dx +e; ax^2 - b

Explanation:

You know it has to be one of the even functions (ax^6 OR ax^4 - bx^3 - cx^2 - dx +e OR ax^2 - b) because the end behaviors are the same.

You could also solve this by just picking a random integer for a and plugging into a graphic calculator!