##<b>Function terminology.</b> Let $f:A\to B$ be a function, i.e. a map that associates with each $x \in A$ a unique $f(x) \in B$. Usually $A$ is a subset of $\m R$ and $B=\m R$.<br> #The <i>domain</i> of $f$ is the set $A$ <br> #The <i>codomain</i> of $f$ is the set $B$ <br> #The <i>range</i> of $f$ is $\{f(x)\ |\ x \in A\}$ <br> #The <i>graph</i> 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 <i>even</i> if $f(-x)=f(x)$ for all $x\in A$ #$f$ is <i>odd</i> if $f(-x)=-f(x)$ for all $x\in A$ #$f$ is <i>increasing</i> on an interval $I$ if for all $x_1<x_2$ in $I$ we have $f(x_1)<f(x_2) #$f$ is <i>decreasing</i> on an interval $I$ if for all $x_1<x_2$ in $I$ we have $f(x_1)>f(x_2)