\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus
Please login to create an exam or a quiz.
Draw/sketch the end behavior that best describes \begin{equation*}f(x) = 44 x^{15} - 42 x^{14} + 7 x^{13} + 3 x^{2} - 16\end{equation*}
The coefficient is \(\displaystyle a_n=44\) and is positive. The degree is \(\displaystyle 15\) and is odd. So the end behavior is
\begin{tikzpicture}
\draw[-latex,domain=0:-1] plot ({\x-.25},{-1*\x*\x});
\draw[-latex,domain=0:1] plot ({\x+.25},{\x*\x});%pos odd
\end{tikzpicture}
\begin{question}Draw/sketch the end behavior that best describes
\begin{equation*}f(x) = 44 x^{15} - 42 x^{14} + 7 x^{13} + 3 x^{2} - 16\end{equation*}
\soln{5cm}{The coefficient is $a_n=44$ and is positive. The degree is $15$ and is odd. So the end behavior is
\begin{tikzpicture}
\draw[-latex,domain=0:-1] plot ({\x-.25},{-1*\x*\x});
\draw[-latex,domain=0:1] plot ({\x+.25},{\x*\x});%pos odd
\end{tikzpicture}
}
\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>Draw/sketch the end behavior that best describes
<img class="equation_image" title=" f(x) = 44 x^{15} - 42 x^{14} + 7 x^{13} + 3 x^{2} - 16 " src="/equation_images/%20f%28x%29%20%3D%2044%20x%5E%7B15%7D%20-%2042%20x%5E%7B14%7D%20%2B%207%20x%5E%7B13%7D%20%2B%203%20x%5E%7B2%7D%20-%2016%20" alt="LaTeX: f(x) = 44 x^{15} - 42 x^{14} + 7 x^{13} + 3 x^{2} - 16 " data-equation-content=" f(x) = 44 x^{15} - 42 x^{14} + 7 x^{13} + 3 x^{2} - 16 " /> </p> </p><p> <p>The coefficient is <img class="equation_image" title=" \displaystyle a_n=44 " src="/equation_images/%20%5Cdisplaystyle%20a_n%3D44%20" alt="LaTeX: \displaystyle a_n=44 " data-equation-content=" \displaystyle a_n=44 " /> and is positive. The degree is <img class="equation_image" title=" \displaystyle 15 " src="/equation_images/%20%5Cdisplaystyle%2015%20" alt="LaTeX: \displaystyle 15 " data-equation-content=" \displaystyle 15 " /> and is odd. So the end behavior is
<?xml version="1.0" encoding="UTF-8"?>
<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="71.251pt" height="57.064pt" viewBox="0 0 71.251 57.064" version="1.1">
<defs>
<clipPath id="clip1">
<path d="M 0 22 L 35 22 L 35 57.0625 L 0 57.0625 Z M 0 22 "/>
</clipPath>
<clipPath id="clip2">
<path d="M 37 0 L 71.25 0 L 71.25 35 L 37 35 Z M 37 0 "/>
</clipPath>
<clipPath id="clip3">
<path d="M 67 0 L 71.25 0 L 71.25 5 L 67 5 Z M 67 0 "/>
</clipPath>
</defs>
<g id="surface1">
<g clip-path="url(#clip1)" clip-rule="nonzero">
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -7.085938 0.00075 L -8.265625 -0.0500312 L -9.449219 -0.194562 L -10.628906 -0.440656 L -11.808594 -0.788312 L -12.992188 -1.229719 L -14.171875 -1.772687 L -15.351563 -2.409406 L -16.535156 -3.147687 L -17.714844 -3.983625 L -18.894531 -4.917219 L -20.074219 -5.952375 L -21.257813 -7.085187 L -22.4375 -8.31175 L -23.617188 -9.639875 L -24.800781 -11.065656 L -25.980469 -12.593 L -27.160156 -14.214094 L -28.339844 -15.93675 L -29.523438 -17.757062 L -30.703125 -19.675031 L -31.882813 -21.690656 L -33.066406 -23.807844 L -34.246094 -26.022687 L -33.796875 -25.139875 " transform="matrix(1,0,0,-1,35.625,28.532)"/>
</g>
<path style=" stroke:none;fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;" d="M 0.199219 56.863281 C 0.859375 56.007812 2.175781 54.742188 3.34375 53.996094 L 0.679688 52.636719 C 0.757812 54.019531 0.503906 55.828125 0.199219 56.863281 "/>
<g clip-path="url(#clip2)" clip-rule="nonzero">
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 7.085937 0.00075 L 8.265625 0.047625 L 9.449219 0.196063 L 10.628906 0.442156 L 11.808594 0.785906 L 12.992187 1.231219 L 14.171875 1.770281 L 15.351562 2.410906 L 16.535156 3.149188 L 17.714844 3.985125 L 18.894531 4.918719 L 20.074219 5.949969 L 21.257812 7.082781 L 22.4375 8.31325 L 23.617187 9.641375 L 24.800781 11.067156 L 25.980469 12.590594 L 27.160156 14.215594 L 28.339844 15.93825 L 29.523437 17.758563 L 30.703125 19.676531 L 31.882812 21.692156 L 33.066406 23.805438 L 34.246094 26.020281 L 33.796875 25.137469 " transform="matrix(1,0,0,-1,35.625,28.532)"/>
</g>
<g clip-path="url(#clip3)" clip-rule="nonzero">
<path style=" stroke:none;fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;" d="M 71.050781 0.199219 C 70.390625 1.054688 69.074219 2.320312 67.90625 3.066406 L 70.570312 4.425781 C 70.492188 3.046875 70.746094 1.234375 71.050781 0.199219 "/>
</g>
</g>
</svg>
</p> </p>