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 $x \to -\infty$, $f(x) \to +\infty$. Opposite end behavior means the degree is odd.

Step2: Check symmetry for function parity

Test if $f(-x) = -f(x)$: the graph is symmetric about the origin. For every point $(a,b)$ on the graph, $(-a,-b)$ is also on the graph. This matches the definition of an odd function.

Answer:

The degree of the function is odd, and the function itself is odd.