Question

the function $f(x)$ is graphed below. determine whether the degree of the function is even or odd and whether the function itself is even or odd.

Explanation:

Step1: Analyze end behavior

As $x\to+\infty$, $f(x)\to+\infty$; as $x\to-\infty$, $f(x)\to-\infty$. For polynomial functions, opposite end behavior means the degree is odd.

Step2: Check symmetry for odd/even function

An odd function satisfies $f(-x) = -f(x)$ (symmetric about the origin), and an even function satisfies $f(-x)=f(x)$ (symmetric about the y-axis). The graph is not symmetric about the y-axis, and it does not have origin symmetry (e.g., $f(1)$ is positive, but $f(-1)$ is not the negative of $f(1)$; the graph near $x=1$ and $x=-1$ does not match origin symmetry). So the function is neither even nor odd.

Answer:

The degree of the function is odd, and the function itself is neither even nor odd.