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\centerline{MATH 133 -- Calculus with Fundamentals 1}
\centerline{Sample Questions for Exam 1}
\centerline{September 22, 2015}
\vskip 10pt
\noindent
I.  Express the set of $x$ satisfying $|2x - 5| > 1$ as an interval or union of intervals.
\vskip 10pt
\noindent
II.  The following table contains values for
three different functions: $f(x),g(x),h(x)$.  
$$\begin{array}{ccccccc}
x  &\vline&0   &0.1  &0.2  &0.3   &0.4\\ \hline
       f(x)  &\vline&-4.2&-5.9 &-7.6 &-9.3  &-11.0\\
       g(x)  &\vline&10   &20    &40    &80 &160\\
       h(x)  &\vline&4   &2.3  &1.5  &2.1   &6.1
\end{array}$$
\begin{enumerate}
\item[A)]  (10) One of these is a linear function. 
Explain how you can tell which one it is, and give a formula for it.
\item[B)]  (10)  One of these functions is {\it neither linear
nor exponential}.  Explain which one that is and why.
\end{enumerate}
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\noindent
III. 
\begin{enumerate}
\item[A)] Complete the square in the quadratic function $f(x) = -3 x^2 + 12 x + 21$.  
\item[B)] What is the maximum value attained by the function $f(x)$.   
\item[C)] Using your answer from part A), sketch the graph $y = -3 x^2 + 12 x + 21$.
\end{enumerate}
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\noindent
IV.  You start at $x = 0$ at time $t = 0$ (hours) and drive along the $x$-axis
($x$ values in miles) at 40 miles an hour for 2 hours.  At $t = 2$ you stop for one hour.
Then starting at $t = 3$, you retrace your earlier path 
and return to your starting position at 80 miles per hour. 
\begin{enumerate} 
\item[A)] Sketch the graph of your position as a function of time.
\item[B)] Give (piecewise) formulas for your function
on the appropriate $t$-intervals. 
\end{enumerate}

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\caption{Figure for Question V}
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\noindent
V.  
\begin{enumerate}
\item[A)] Express the domain of the function $f(x) = \frac{x}{x^2 - 1}$ as a union of intervals.
\item[B)] Figure 1 on the back of this page shows the graph $y = \frac{x}{x^2 - 1}$.  Based on this, what can you 
say about the range of $f(x)$?
\item[C)] Does $f(x)$ have an inverse function?  Why or why not?
\end{enumerate}
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\noindent
VI.  
\begin{enumerate}
\item[A)] Sketch the graph of $y = 3\sin\left(\frac{x}{2}\right) + 2$ for $0 \le x \le 8\pi$.  
\item[B)] What are the \emph{amplitude} and \emph{period} of this sinusoidal function?
\end{enumerate}
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\noindent
VII.  
\begin{enumerate}
\item[A)]  Simplify:  $\log_3(27) + \ln(e^{-3})$.  
\item[B)]  The population of a city (in millions) at time $t$ (years) is $P(t) = 2.4 e^{0.06 t}$.  What is 
the population at $t = 0$?  When will the population reach $4$ million?
\end{enumerate}
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