**Function terminology.**
Let $f:A\to B$ be a function, i.e. a map that associates with each $x
\in A$ a unique $f(x) \in B$. In single variable
Calculus, usually $A$ is a subset of $\m R$ and
$B=\m R$.

The *domain* of $f$ is the set $A$

The *codomain* of $f$ is the set $B$

The *range* of $f$ is $\{f(x)\ |\ x \in A\}$

The *graph* of $f$ is $\{(x,f(x))\ |\ x\in A\}$

A curve in the $xy$-plane is the graph of a function if and only if no vertical line intersects the curve more than once (the vertical line test).

Two functions $f$ and $g$ are equal if they have the same domain and $f(x)=g(x)$ for all $x\in A$

$f$ is *even* if $f(-x)=f(x)$ for all $x\in A$

$f$ is *odd* if $f(-x)=-f(x)$ for all $x\in A$

$f$ is *increasing* on an interval $I$ if for all $x_1 < x_2$ in
$I$ we have $f(x_1) < f(x_2)$

$f$ is *decreasing* on an interval $I$ if for all $x_1 < x_2$ in
$I$ we have $f(x_1) > f(x_2)$