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\centerline{\textbf{\large Graphing Quiz $\cdot$ Monday October 23, 2006}}
\vspace*{.2in}
MATH 111 $\cdot$ Section 7 $\cdot$ Fall 2006  \hspace*{0.5in} Name \hrulefill
\vspace*{0.2in}

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\textbf{Problem 1.} Using the space provided, sketch EXACTLY TWO PERIODS
of $y=\sin(x)$.  Do not change the numbering on the horizontal axis.
\vspace*{2.7in}

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\textbf{Problem 2.} Using the space provided, sketch EXACTLY TWO PERIODS
of $y=\cos(x)$.  Do not change the numbering on the horizontal axis.
\vspace*{2.7in}

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\textbf{Problem 3.} Using the space provided, sketch EXACTLY TWO PERIODS
of $y=\tan(x)$.  Do not change the numbering on the horizontal axis.
\vspace*{2.7in}

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\textbf{Problem 4.} Using the space provided, sketch EXACTLY TWO PERIODS of
$$y=1+2\sin(\pi x /2 - \pi/2).$$  Do not change the numbering on the horizontal
axis.
\vspace*{2.7in}

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\textbf{Problem 5.}  Consider the following data table containing points from
a sine function:
$$
\begin{tabular}{|l||r|r|r|r|r|r|r|}
\hline $x$    & 2 & 4 & 6 & 8 & 10 & 12 \\
\hline $f(x)$ & 7 & 8 & 9 & 8 &  7 &  8 \\
\hline
\end{tabular}
$$

\textbf{Part (a)}  Sketch a graph of this function.
\vspace*{2.0in}

\textbf{Part (b)}  From your graph in part (a), determine the following
quantities:
\vspace*{0.2in}

\begin{tabular}{ll}
Amplitude:     & \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ \\
Average value: & \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ \\
Period:        & \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ \\
Phase shift:   & \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\
\end{tabular}
\vspace*{0.2in}

\textbf{Part (c)}  Using the values you determined in part (b), write an
equation of a sine function (in the form $y=a + b \sin(cx+d)$) which models
these data.

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