Answer
See below.
Work Step by Step
"Even" and "odd" terms come from the powers of x of functions defined with $f(x)=x^{n}$, where n is a nonnegative integer. Even n's result in graphs symmetric to the y-axis; odd n's result in graphs symmetric to the origin.
A graph of a function consists of points (x, f(x)).
The graphs of even functions are symmetric about the y-axis, meaning that $x$ and$ -x$ have the same function value; that is, $f(-x)=f(x)$.
If $(x,y)$ lies on the graph, so does $(-x, y)$.
The graphs of odd functions are symmetric about the origin; that is,
$f(x)=-f(x)$
If $(x,y)$ lies on the graph, so does $(-x, -y).$
The advantage of finding out that a function is odd or even is that we can graph one side of the origin, and apply symmetry to graph the other side.
(We calculate the function values for positive x by applying the formula for f(x). We do not need to calculate $f(-x)$ by applying the formula.)
Examples:
$f(x)=x^{2}$ is an even function, $f(x)=x^{3}$ is an odd function.
$f(x)=(x-1)^{2}$ is neither odd nor even because, for example:
$f(2)=1,$ but $f(-2)=9$
Since $f(-x)\neq f(x)$ for all x, the function is not even.
Since $f(-x)\neq-f(x)$ for all x, the function is not odd.
