Algebra-2

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

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

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

Implications of the End Behavior:

Since both ends of the graph go to infinity, we can conclude that:

The polynomial has an even degree (even-degree polynomials have the same behavior on both ends).

The leading coefficient must be positive (to ensure that both ends go upwards).

Evaluating the Options:

A. Positive coefficient, even degree:

Correct: This option matches the observed behavior perfectly. When a polynomial has an even degree and a positive leading coefficient, as  approaches positive or negative infinity,  approaches positive infinity.

B. Positive coefficient, odd degree:

Incorrect: For an odd-degree polynomial with a positive leading coefficient, as ,

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