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\begin{document}
\begin{center}
{\textbf{\Large Math 010 Practice Problems for Test 2 Fall 2022}}
\end{center}
\begin{singlespacing}
The following are examples of potential exam questions. It is recommended that you show all work while doing these problems. No problem requires a calculator but you are welcome to use one.

\begin{enumerate}
\item Mid point and distance\\
Examples:
\begin{enumerate}
\item Compute the mid point and the distance of these two points $(0,0)$ and $(2,0)$
\vspace{5cm}
\item Compute the mid point and the distance of these two points $(1,1)$ and $(2,2)$
\vspace{5cm}
\item Compute the mid point and the distance of these two points $(-5,3)$ and $(3,-7)$
\vspace{5cm}
\end{enumerate}

\item
Distinguish between functions and relations
using the Vertical Line Test\\
Examples:
\begin{enumerate}
\item Determine if the relation is a function $(1,2),(2,2),(3,2),(4,2)$
\vspace{5cm}
\item Determine if the relation is a function $(2,1),(2,2),(2,3),(2,4)$
\vspace{5cm}
\item Determine if the relation is a function $(1,2),(3,5),(5,3),(7,7)$
\vspace{5cm}
\item Determine if the picture below is a function.

\includegraphics[scale=.5]{circle2.png}
\item Determine if the picture below is a function.

\includegraphics[scale=.5]{sinx.png}
\end{enumerate}


\item 
Identify the domain and range of a function\\
Examples:
\begin{enumerate}
\item Determine the domain and range of this function.

\includegraphics[scale=.5]{x2.png}

\item Determine the domain and range of this function.

\includegraphics[scale=.5]{x2-2.png}

\item Determine the domain and range of this function.

$f(x)=\sqrt{x}-3$
\vspace{5cm}

\item Determine the domain and range of this function.

$f(x)=(x+4)^2-3$
\vspace{5cm}

\end{enumerate}

\item 
Graphing functions\\
Examples:
\begin{enumerate}
\item Graph using a table and describe the shift from the parent function:\\ $f(x)=(x-3)^2-2$
\vspace{5cm}
\item Graph using a table and describe the shift from the parent function:\\ $f(x)=|x+2|+3$
\vspace{5cm}
\item Graph using a table and describe the shift from the parent function:\\ $f(x)=\sqrt{x-2}+3$
\vspace{5cm}


\end{enumerate}

\item 
Solving linear equations\\
Examples:
\begin{enumerate}
\item Solve for x:
$4(x-2)=12$
\vspace{5cm}
\item Solve for x:
$12+2(5-3x)=-9(x-1)-2$
\vspace{5cm}
\item Solve for x:
$\frac{1}{4}x+\frac{1}{2}=-\frac{3}{4}$
\vspace{5cm}
\item Solve for x:
$\frac{1}{2}x+\frac{3}{8}=\frac{3}{4}$
\vspace{5cm}
\end{enumerate}

\item 
Graphing a linear function using slope and y-intercept\\
Examples:
\begin{enumerate}
\item Graph $f(x)=5$ using slope and y-intercept
\vspace{5cm}
\item Graph $f(x)=x+2$ using slope and y-intercept
\vspace{5cm}
\item Graph $f(x)=3x-4$ using slope and y-intercept
\vspace{5cm}
\item Graph $f(x)=-2x+1$ using slope and y-intercept
\vspace{5cm}
\end{enumerate}


\item 
Finding the slope\\
Examples:
\begin{enumerate}
\item Find the slope between $(0,0)$ and $(2,0)$
\vspace{5cm}
\item Find the slope between $(1,1)$ and $(2,2)$
\vspace{5cm}
\item Find the slope between $(-5,3)$ and $(3,-7)$
\vspace{5cm}
\item Find the slope between $(2,1)$ and $(4,6)$
\vspace{5cm}
\end{enumerate}

\item 
Slope intercept\\
Examples:
\begin{enumerate}
\item Find the equation of a line in slope-intercept form with slope $\frac{1}{3}$ and going through the point $(0,-6)$. 
\vspace{5cm}
\item Find the equation of a line in slope-intercept form with slope $2$ and going through the point $(1,3)$. 
\vspace{5cm}
\item Find the equation of a line in slope-intercept form with slope $-\frac{5}{2}$ and going through the point $(2,7)$. 
\vspace{5cm}
\item Find the equation of a line in slope-intercept form with slope $-3$ and going through the point $(4,-7)$. 
\vspace{5cm}
\end{enumerate}

\item 
Parallel and perpendicular lines\\
Examples:
\begin{enumerate}
\item Find the equation of the line parallel to $y=2x+1$ and containing the point $(0,0)$
\vspace{5cm}
\item Find the equation of the line parallel to $6x-3y=9$ and containing the point $(0,-4)$
\vspace{5cm}
\item Find the equation of the line perpendicular to $y=3x+1$ and containing the point $(0,3)$.
\vspace{5cm}
\item Find the equation of the line perpendicular to $x+5y=-10$ and containing the point $(0,-2)$.
\vspace{5cm}

\end{enumerate}


\end{enumerate}
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