\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Suppose $f(x)$ is a piecewise
function defined as follows:

$$ f(x) = \cases {2x^2+2, &if $x<1$\cr ax^2+bx, &if $1 \le x \le 2$\cr
2-{{\textstyle 6\vphantom{A^2b_B}}\over{\textstyle x}\vphantom{2^>b_J}}, &if $x > 2$\cr}.
$$
\smallskip
\noindent a) Suppose that $a=2$ and $b=-3$. Graph $f(x)$ for $0 \leq x
\leq 3$.  Find the left and right hand limits of $f(x)$ as $x$
approaches $1$ and as $x$ approaches $2$.

\medskip

\noindent b) Find $a$ and $b$ so that the graph of $f(x)$ doesn't have
any jumps (that is, $f(x)$ is continuous everywhere). Graph the
resulting function $f(x)$ for $0 \leq x \leq 3$.
 









\vfil\eject\end

