Question

END BEHAVIOR:
n is even and a>0, ends will go ___ and ___

Answer 1

The end behavior of a polynomial where the degree is even (n is even) and the leading coefficient is positive (a>0) is such that both ends of the graph will go upwards.

Step-by-step explanation:

The student's question relates to the end behavior of polynomial functions when the leading coefficient is positive (a>0) and the degree of the polynomial (n) is even. In such cases, both ends of the graph of the polynomial function will point in the same direction. Since the leading coefficient is positive (a>0), the ends of the graph will go upwards.

Here's a step-by-step explanation:

1. An even-degree polynomial will have a similar end behavior at both ends.
2. If the leading coefficient is positive, the graph will rise to infinity as it moves away from the origin in both the positive and negative x-directions.
3. Therefore, for a polynomial function where n is even and a is positive, the ends will both go up.