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.\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.\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

As (x\to-\infty), (y\to-\infty) and as (x\to+\infty), (y\to+\infty). For a polynomial function (y = f(x)=a_nx^n+\cdots+a_0), when the end - behaviors are in opposite directions (one goes to (-\infty) and the other to (+\infty)), the degree (n) is odd.

Step2: Check for function parity

A function (y = f(x)) is even if (f(-x)=f(x)) (symmetric about the y - axis) and odd if (f(-x)=-f(x)) (symmetric about the origin). The graph of the function is not symmetric about the y - axis (so it's not even). Also, if we take a point ((x,y)) on the graph and check ((-x,-y)), we can see that the graph is not symmetric about the origin. For example, the function value at (x = 1) and (x=-1) does not satisfy the odd - function property.

Answer:

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