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\hskip36pc \= Math.\ 302-01\\
\>Spring, 2005\\
\>R. B. Kearfott
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\begin{center}
\bf First Examination \\
\it Monday, January 24, 2005
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\noindent {\small {\bf Instructions:} This exam should be done on
your own paper. Your name should be on each sheet and on the back
of the last sheet; the answers should appear written carefully and
in order. If in doubt, show intermediate steps: Full credit may
not be given, even for correct answers, unless work is arranged
clearly and explained. This exam is closed book. You may leave
after handing in your exam paper, but be sure to check your
answers carefully. Each entire problem is worth 30 points, while
10 points are free.}

\begin{enumerate}
   \item State which of the following tables can correspond to linear
         functions.  For those that can correspond to a linear
         function, write down the function.  For those that cannot
         correspond to a linear function, explain why not.
         $$\begin{array}{rcrc}
               \mbox{a)} &
               \begin{array}{|r||r|r|r|r|r|}
               \hline
               & y = -4 & y = -2 & y = 0 & y = 2 & y = 4 \\
               \hline\hline
         x = 1 &   -6  &   0  &   6 &   12  &  18 \\ \hline
         x = 2 &   -4  &   2  &   8 &   14  &  20 \\ \hline
         x = 3 &   -2  &   4  &  10 &   16  &  22 \\ \hline
         x = 4 &    0  &   6  &  12 &   18  &  24 \\ \hline
         x = 5 &    2  &   8  &  14 &   20  &  26 \\ \hline
               \end{array} &
               \mbox{b)} &
         \begin{array}{|r||r|r|r|r|r|}
               \hline
               & y = -4 & y = -2 & y = 0 & y = 2 & y = 4 \\
               \hline\hline
         x = 1 &  -7 &   -3 &    1  &   5 &    9   \\ \hline
         x = 2 & -10 &   -4 &    2  &   8 &   14   \\ \hline
         x = 3 & -13 &   -5 &    3  &  11 &   19   \\ \hline
         x = 4 & -16 &   -6 &    4  &  14 &   24   \\ \hline
         x = 5 & -19 &   -7 &    5  &  17 &   29   \\ \hline
               \end{array}
         \end{array}$$
   \item Write down a linear function that can correspond to the
         following contour diagram. \newline
         \hskip1in{\mbox{\includegraphics[scale=0.3]{tst1fig1.eps}}}
   \item \begin{enumerate}
         \item Write down an equation for the set of all points whose distance
               from the $xy$-plane is equal to the square of the
               point's distance from the $z$-axis.
         \item Describe the graph of this equation, i.e. describe
               this set of points.
         \item Sketch a rough graph of this set of points.
         \end{enumerate}
\end{enumerate}

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