\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Suppose $f(x)=\big|x - |x-3|
\big|\,$. $f(x)$ is defined for all real numbers. 

\medskip

\noindent a) Find the graph of $y=f(x)$ in the window $-5\le x\le 5$
and $0\le y\le 10\,$.

\medskip

\noindent b) Give a piecewise definition (on all of its domain) of
$f(x)$ {\it without}\/ using absolute value. The graph may help to
answer this question, but justify your answer algebraically with a
case-by-case argument from the equation for $y$. Your justification
could begin with a statement such as, ``When $x \ge 3$, then $y$ is
given by the formula $\ldots$ because $\ldots$''.

\vfil\eject\end