Question

What is the end behavior f(x) ?

Answer 1

Answer: Choice C)

$\text{ as } x \to \infty, \ f(x) \to \infty\\\\\text{ as } x \to -\infty, \ f(x) \to -\infty$

In other words, as x gets really large in the positive direction, so does f(x).

As x gets really large in the negative direction, so does f(x). We can see that x and f(x) move in the same direction toward the same type of infinity.

In laymen's terms or in plain English, we can say that "The graph falls to the left and rises to the right". We don't worry about the wiggle motion in the middle, since all we care about is what's going on as x goes to either infinity.

"Falls to the left" means it goes down forever as we move leftward. "Rises to the right" means it goes up forever as we move to the right. This type of behavior of "falls to the left and rises to the right" is indicative of any odd degree polynomial where the leading coefficient is positive. In this case, it appears we're dealing with a cubic function of degree 3.