Question

what is the degree? options: even, positive, negative, odd (with a graph of a polynomial function)

Explanation:

To determine the degree type (even or odd) of a polynomial from its graph, we check the end - behavior and symmetry. For an even - degree polynomial, the ends of the graph either both go up or both go down (symmetric about the y - axis in the case of even functions, but more generally, the end - behavior is symmetric with respect to the vertical direction). For an odd - degree polynomial, the ends go in opposite directions (one up and one down). Looking at the given graph, as \(x\to+\infty\) and \(x\to-\infty\), the graph's ends both go up (or we can also consider the number of turning points and the general shape). The graph has a shape consistent with an even - degree polynomial. The options "Positive" and "Negative" refer to the leading coefficient's sign, not the degree type. So the degree type is even.

Answer:

A. Even