\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus
Please login to create an exam or a quiz.
List all transformations of \(\displaystyle f(x)=x^{2}\) to obtain the graph of \(\displaystyle g(x)=2 \left(x - 7\right)^{2}+10\)
The graph is stretched by a factor of \(\displaystyle 2\). The graph is shifted right 7 units. The graph is shifted up 10 units.
\begin{question}List all transformations of $f(x)=x^{2}$ to obtain the graph of $g(x)=2 \left(x - 7\right)^{2}+10$
\soln{9cm}{The graph is stretched by a factor of $2$. The graph is shifted right 7 units. The graph is shifted up 10 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^{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)=2 \left(x - 7\right)^{2}+10 " src="/equation_images/%20%5Cdisplaystyle%20g%28x%29%3D2%20%5Cleft%28x%20-%207%5Cright%29%5E%7B2%7D%2B10%20" alt="LaTeX: \displaystyle g(x)=2 \left(x - 7\right)^{2}+10 " data-equation-content=" \displaystyle g(x)=2 \left(x - 7\right)^{2}+10 " /> </p> </p><p> <p>The graph is stretched by a factor of <img class="equation_image" title=" \displaystyle 2 " src="/equation_images/%20%5Cdisplaystyle%202%20" alt="LaTeX: \displaystyle 2 " data-equation-content=" \displaystyle 2 " /> . The graph is shifted right 7 units. The graph is shifted up 10 units.</p> </p>