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List all transformations of \(\displaystyle f(x)=x^{2}\) to obtain the graph of \(\displaystyle g(x)=- 3 \left(x - 4\right)^{2}-1\)

The graph is reflected across the \(\displaystyle x\) axis. The graph is stretched by a factor of \(\displaystyle 3\). The graph is shifted right 4 units. The graph is shifted down 1 units.

Download \(\LaTeX\)

\begin{question}List all transformations of $f(x)=x^{2}$ to obtain the graph of $g(x)=- 3 \left(x - 4\right)^{2}-1$
    \soln{9cm}{The graph is reflected across the $x$ axis. The graph is stretched by a factor of $3$. The graph is shifted right 4 units.  The graph is shifted down 1 units.}

\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%
}%
\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
\else%
#1%
\fi%
}%
\everymath{\displaystyle}
\ShowSolutiontrue

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

\end{question}\end{document}

List all transformations of <img class="equation_image" title=" \displaystyle f(x)=x^{2} " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%3Dx%5E%7B2%7D%20" alt="LaTeX: \displaystyle f(x)=x^{2} " data-equation-content=" \displaystyle f(x)=x^{2} " /> to obtain the graph of <img class="equation_image" title=" \displaystyle g(x)=- 3 \left(x - 4\right)^{2}-1 " src="/equation_images/%20%5Cdisplaystyle%20g%28x%29%3D-%203%20%5Cleft%28x%20-%204%5Cright%29%5E%7B2%7D-1%20" alt="LaTeX: \displaystyle g(x)=- 3 \left(x - 4\right)^{2}-1 " data-equation-content=" \displaystyle g(x)=- 3 \left(x - 4\right)^{2}-1 " />

The graph is reflected across the <img class="equation_image" title=" \displaystyle x " src="/equation_images/%20%5Cdisplaystyle%20x%20" alt="LaTeX: \displaystyle x " data-equation-content=" \displaystyle x " /> axis. The graph is stretched by a factor of <img class="equation_image" title=" \displaystyle 3 " src="/equation_images/%20%5Cdisplaystyle%203%20" alt="LaTeX: \displaystyle 3 " data-equation-content=" \displaystyle 3 " /> . The graph is shifted right 4 units. The graph is shifted down 1 units.