Algebra-2

From the graph, it can be seen that as and as . The ends go in the different direction.

As ( ): The right end of the graph goes up.

As ( ): The left end of the graph goes down.

Implications of the End Behavior:

Since the ends go in different directions (one goes up and the other goes down), we can conclude that:

The polynomial must have an odd degree (only odd-degree polynomials have ends that go in opposite directions).

The leading coefficient must be positive (this will ensure that the right end goes up and the left end goes down).

Evaluating the Options:

A. Positive coefficient, even degree:

Incorrect: An even-degree polynomial with a positive leading coefficient has both ends going up ( as