The graph of a polynomial is shown. Which end-behavior statement is consistent with the graph?

Answer and derivation

Correct answer: B

Both ends rise, so $p(x)$ approaches positive infinity in both directions.

1. On the far left, decreasing $x$ corresponds to increasing $p(x)$.
2. On the far right, increasing $x$ also corresponds to increasing $p(x)$.
3. This is the even-degree, positive-leading-coefficient end pattern.

Why the other options fail

A

It sends the left tail downward.

B

Correct description of both rising tails.

C

It reverses both tails.

D

It reverses the right tail.

Common misconception: Turning points in the middle do not determine end behavior.

China/AP bridge: Connect the graph to the sign and parity of the leading term.