\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus
Please login to create an exam or a quiz.
List all transformations of \(\displaystyle f(x)=|x|\) to obtain the graph of \(\displaystyle g(x)=- 2 \left|{x - 2}\right| - 6\)
The graph is shifted right 2 units. The graph is reflected across the \(\displaystyle x-\) axis and stretched by a factor of 2. The graph is shifted down 6 units.
\begin{question}List all transformations of $f(x)=|x|$ to obtain the graph of $g(x)=- 2 \left|{x - 2}\right| - 6$
\soln{9cm}{The graph is shifted right 2 units. The graph is reflected across the $x-$ axis and stretched by a factor of 2. The graph is shifted down 6 units.}
\end{question}
\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}<p> <p>List all transformations of <img class="equation_image" title=" \displaystyle f(x)=|x| " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%3D%7Cx%7C%20" alt="LaTeX: \displaystyle f(x)=|x| " data-equation-content=" \displaystyle f(x)=|x| " /> to obtain the graph of <img class="equation_image" title=" \displaystyle g(x)=- 2 \left|{x - 2}\right| - 6 " src="/equation_images/%20%5Cdisplaystyle%20g%28x%29%3D-%202%20%5Cleft%7C%7Bx%20-%202%7D%5Cright%7C%20-%206%20" alt="LaTeX: \displaystyle g(x)=- 2 \left|{x - 2}\right| - 6 " data-equation-content=" \displaystyle g(x)=- 2 \left|{x - 2}\right| - 6 " /> </p> </p><p> <p>The graph is shifted right 2 units. 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 and stretched by a factor of 2. The graph is shifted down 6 units.</p> </p>