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Graph the function \(\displaystyle f(x)=\begin{cases} - \frac{4 x}{5} - 5,& x \leq -2\\ 5 - \frac{x^{2}}{5},& -2 < x < 2\\ x - 7,& x \geq 2 \\ \end{cases}\)

The graph has three parts. It is a line on \(\displaystyle (-\infty, -2]\), a parabola on \(\displaystyle (-2,2)\), and a line on \(\displaystyle [2, \infty)\). Graphing each part gives:

Download Tikz \( \LaTeX \) 

\begin{tikzpicture}[font=\Large, scale=.4]
	\draw[very thick, color=blue, opacity=0.3, xstep=1, ystep=1] (-10,-10) grid (10,10);
	\draw[latex-latex, very thick] (-10.4,0)--(10.4,0) node[right]{$x$};
	\draw[latex-latex, very thick] (0,-10.4)--(0,10.4) node[above]{$y$};
	\foreach \x in { -10,-8,...,10 }{
		\pgfmathsetmacro{\xtick}{\x != 0 ? "\x" : ""}
		\draw (\x, .2) -- (\x,-.2) node[below]{$\xtick$};
		}
	\foreach \y in { -10,-8,...,10 }{
		\pgfmathsetmacro{\ytick}{\y != 0 ? "\y" : ""}
		\draw (.2, \y) -- (-.2, \y) node[left]{$\ytick$};
		}
	\draw[thick, color=blue, domain={-10.0}:{-2.0}, latex-, samples =350] plot(\x, {-4*(\x)/5 - 5});
	\draw[thick, color=blue, domain={-2.0}:{2.0}, samples =350] plot(\x, {5 - (\x)^2/5});
	\draw[thick, color=blue, domain={2.0}:{10.0}, -latex, samples =350] plot(\x, {(\x) - 7});
		\draw[fill=black] (-2,-17/5) circle (5pt);
		\draw[fill=white] (-2,21/5) circle (5pt);
		\draw[fill=white] (2,21/5) circle (5pt);
		\draw[fill=black] (2,-5) circle (5pt);
\end{tikzpicture}

Download \(\LaTeX\) 

\begin{question}Graph the function $f(x)=\begin{cases} - \frac{4 x}{5} - 5,& x \leq -2\\ 5 - \frac{x^{2}}{5},& -2 < x < 2\\ x - 7,& x \geq 2 \\ \end{cases}$\newline
\begin{tikzpicture}[font=\Large, scale=.4]
	\draw[very thick, color=blue, opacity=0.3, xstep=1, ystep=1] (-10,-10) grid (10,10);
	\draw[latex-latex, very thick] (-10.4,0)--(10.4,0) node[right]{$x$};
	\draw[latex-latex, very thick] (0,-10.4)--(0,10.4) node[above]{$y$};
	\foreach \x in { -10,-8,...,10 }{
		\pgfmathsetmacro{\xtick}{\x != 0 ? "\x" : ""}
		\draw (\x, .2) -- (\x,-.2) node[below]{$\xtick$};
		}
	\foreach \y in { -10,-8,...,10 }{
		\pgfmathsetmacro{\ytick}{\y != 0 ? "\y" : ""}
		\draw (.2, \y) -- (-.2, \y) node[left]{$\ytick$};
		}
\end{tikzpicture}

    \soln{0cm}{The graph has three parts. It is a line on $(-\infty, -2]$, a parabola on $(-2,2)$, and a line on $[2, \infty)$.  Graphing each part gives:\newline
\begin{tikzpicture}[font=\Large, scale=.4]
	\draw[very thick, color=blue, opacity=0.3, xstep=1, ystep=1] (-10,-10) grid (10,10);
	\draw[latex-latex, very thick] (-10.4,0)--(10.4,0) node[right]{$x$};
	\draw[latex-latex, very thick] (0,-10.4)--(0,10.4) node[above]{$y$};
	\foreach \x in { -10,-8,...,10 }{
		\pgfmathsetmacro{\xtick}{\x != 0 ? "\x" : ""}
		\draw (\x, .2) -- (\x,-.2) node[below]{$\xtick$};
		}
	\foreach \y in { -10,-8,...,10 }{
		\pgfmathsetmacro{\ytick}{\y != 0 ? "\y" : ""}
		\draw (.2, \y) -- (-.2, \y) node[left]{$\ytick$};
		}
	\draw[thick, color=blue, domain={-10.0}:{-2.0}, latex-, samples =350] plot(\x, {-4*(\x)/5 - 5});
	\draw[thick, color=blue, domain={-2.0}:{2.0}, samples =350] plot(\x, {5 - (\x)^2/5});
	\draw[thick, color=blue, domain={2.0}:{10.0}, -latex, samples =350] plot(\x, {(\x) - 7});
		\draw[fill=black] (-2,-17/5) circle (5pt);
		\draw[fill=white] (-2,21/5) circle (5pt);
		\draw[fill=white] (2,21/5) circle (5pt);
		\draw[fill=black] (2,-5) circle (5pt);
\end{tikzpicture}
}

\end{question}

Download Question and Solution Environment\(\LaTeX\)
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}

\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}

\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}

\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
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\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
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\everymath{\displaystyle}
\ShowSolutiontrue

\begin{document}\begin{question}(10pts) The question goes here!
    \soln{9cm}{The solution goes here.}

\end{question}\end{document}
HTML for Canvas 
<p> <p>Graph the function  <img class="equation_image" title=" \displaystyle f(x)=\begin{cases} - \frac{4 x}{5} - 5,& x \leq -2\\ 5 - \frac{x^{2}}{5},& -2 < x < 2\\ x - 7,& x \geq 2 \\ \end{cases} " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%3D%5Cbegin%7Bcases%7D%20-%20%5Cfrac%7B4%20x%7D%7B5%7D%20-%205%2C%26%20x%20%5Cleq%20-2%5C%5C%205%20-%20%5Cfrac%7Bx%5E%7B2%7D%7D%7B5%7D%2C%26%20-2%20%3C%20x%20%3C%202%5C%5C%20x%20-%207%2C%26%20x%20%5Cgeq%202%20%5C%5C%20%5Cend%7Bcases%7D%20" alt="LaTeX:  \displaystyle f(x)=\begin{cases} - \frac{4 x}{5} - 5,& x \leq -2\\ 5 - \frac{x^{2}}{5},& -2 < x < 2\\ x - 7,& x \geq 2 \\ \end{cases} " data-equation-content=" \displaystyle f(x)=\begin{cases} - \frac{4 x}{5} - 5,& x \leq -2\\ 5 - \frac{x^{2}}{5},& -2 < x < 2\\ x - 7,& x \geq 2 \\ \end{cases} " /> <br>
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HTML for Canvas
<p> <p>The graph has three parts. It is a line on  <img class="equation_image" title=" \displaystyle (-\infty, -2] " src="/equation_images/%20%5Cdisplaystyle%20%28-%5Cinfty%2C%20-2%5D%20" alt="LaTeX:  \displaystyle (-\infty, -2] " data-equation-content=" \displaystyle (-\infty, -2] " /> , a parabola on  <img class="equation_image" title=" \displaystyle (-2,2) " src="/equation_images/%20%5Cdisplaystyle%20%28-2%2C2%29%20" alt="LaTeX:  \displaystyle (-2,2) " data-equation-content=" \displaystyle (-2,2) " /> , and a line on  <img class="equation_image" title=" \displaystyle [2, \infty) " src="/equation_images/%20%5Cdisplaystyle%20%5B2%2C%20%5Cinfty%29%20" alt="LaTeX:  \displaystyle [2, \infty) " data-equation-content=" \displaystyle [2, \infty) " /> .  Graphing each part gives:<br>
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