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

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.\n\nanswer\n$f(x)$ has an even degree, but is not an even function\n$f(x)$ has an even degree and is an even function\n$f(x)$ has an odd degree, but is not an odd function\n$f(x)$ has an odd degree and is an odd function

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.\n\nanswer\n$f(x)$ has an even degree, but is not an even function\n$f(x)$ has an even degree and is an even function\n$f(x)$ has an odd degree, but is not an odd function\n$f(x)$ has an odd degree and is an odd function

Answer

Explanation:

Step1: Analyze end behavior for degree parity

Both ends of the graph point downwards as $x \to \infty$ and $x \to -\infty$, indicating an even degree.

Step2: Check for y-axis symmetry

The graph is not symmetric about the y-axis (e.g., $f(4) \approx -10$ while $f(-4) \approx -100$), so it is not an even function.

Step3: Check for origin symmetry

The graph does not have rotational symmetry about the origin, so it is not an odd function.

Step4: Combine findings

The function has an even degree but is not an even function.

Answer:

$f(x)$ has an even degree, but is not an even function