\input epsf
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\noindent {\bf Problem statement} a) Suppose that $f(x)=x^2$ and
$g(x)=2^x$. Compute $f(-2)$, $g(-2)$, $f(5)$, and $g(5)$. According to
the Intermediate Value Theorem and the function values computed, what
is the smallest number of roots the equation $f(x)=g(x)$ can have?

\medskip \noindent
b) Suppose still that $f(x)=x^2$ and $g(x)=2^x$. Graph $y=f(x)$ and
$y=g(x)$ carefully on the interval $-2\le x\le 5$. How many roots does
the equation $f(x)=g(x)$ appear to have?
\medskip \noindent
c) Draw graphs of two increasing continuous functions which intersect
exactly two times.
\medskip \noindent
d) Draw graphs of two increasing continuous functions which intersect
exactly three times.
\medskip \noindent
e) Draw graphs of two increasing continuous functions which intersect
exactly four times.







\vfil\eject\end

