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\noindent {\bf Problem statement} Suppose $f$ is the function defined
by $f(x) = |x - 1|.$

\medskip

\noindent a) Sketch the graph of $y = f(x)$. 

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\noindent b) Sketch the graph of $y = {(f \circ f)(x) } = {f(f(x))}$.

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\noindent c) Suppose $g$ is the function defined by $g(x) = |x - 2| +
|x+3| - 2|x - 1|$. Sketch the graph of $y= g(x)$.

\medskip

\noindent d) What can you conclude about the behavior of $g(x)$ when
$x$ is large positive? What about when $x$ is large negative? Verify
your assertions using algebra.

\smallskip

\noindent {\it Suggestion:} Work on the intervals $ (-\infty,-3]$ and
$[2,\infty)$ and get algebraic formulas for $g(x)$ on each interval
which do not involve absolute value.



%inspired by a problem of Michael O'Nan







\vfil\eject\end

