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

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. answer: f(x) has an odd degree and is an odd function; f(x) has an odd degree, but is not an odd function; f(x) has an even degree and is an even function; f(x) has an even degree, but is not an even 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. answer: f(x) has an odd degree and is an odd function; f(x) has an odd degree, but is not an odd function; f(x) has an even degree and is an even function; f(x) has an even degree, but is not an even function

Answer

Explanation:

Step1: Check end - behavior

As (x\to+\infty), (y\to+\infty) and as (x\to - \infty), (y\to-\infty). For a polynomial function (y = a_nx^n+\cdots+a_0), when the degree (n) is odd, the end - behaviors are opposite. When (n) is even, the end - behaviors are the same (both (y\to+\infty) or both (y\to-\infty) as (x\to\pm\infty)). So the degree of the function is odd.

Step2: Check for odd - function property

An odd function satisfies (f(-x)=-f(x)), which means its graph is symmetric about the origin. The given graph passes through the origin ((0,0)) and has rotational symmetry about the origin. So it is an odd function.

Answer:

The function (f(x)) has an odd degree and is an odd function.