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**sfspitfire23** If $\displaystyle f:I\rightarrow R$ and $\displaystyle g: \rightarrow R$ are any functions defined on $\displaystyle I$, then we can form new functions $\displaystyle max\{f,g\}(x)=max\{f(x),g(x)\}$ for all $\displaystyle x\in I$, and similarly for $\displaystyle min\{f,g\}$

I'm asked to sketch a graph of $\displaystyle max\{f,g\}$ and $\displaystyle min\{f,g}$ if $\displaystyle f(x)=sin x$ and $\displaystyle g(x)=cos x$ on $\displaystyle I=[-2\pi , 2\pi ]$

What do the max/min thing mean? Basically, what is the first paragraph telling me? Thanks for any help.