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Questions: Algebra BusinessCalculus
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Draw/sketch the end behavior that best describes \begin{equation*}f(x) = - 16 x^{19} - 14 x^{18} - 8 x^{17} - 82 x^{15} - 27 x^{11} + 7 x^{8} + 14\end{equation*}
The coefficient is \(\displaystyle a_n=-16\) and is negative. The degree is \(\displaystyle 19\) and is odd. So the end behavior is
\begin{tikzpicture}
\draw[-latex,domain=0:-1] plot ({\x-.25},{\x*\x});
\draw[-latex,domain=0:1] plot ({\x+.25},{-1*\x*\x});%neg odd
\end{tikzpicture}
\begin{question}Draw/sketch the end behavior that best describes
\begin{equation*}f(x) = - 16 x^{19} - 14 x^{18} - 8 x^{17} - 82 x^{15} - 27 x^{11} + 7 x^{8} + 14\end{equation*}
\soln{5cm}{The coefficient is $a_n=-16$ and is negative. The degree is $19$ and is odd. So the end behavior is
\begin{tikzpicture}
\draw[-latex,domain=0:-1] plot ({\x-.25},{\x*\x});
\draw[-latex,domain=0:1] plot ({\x+.25},{-1*\x*\x});%neg odd
\end{tikzpicture}
}
\end{question}
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\everymath{\displaystyle}
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\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) = - 16 x^{19} - 14 x^{18} - 8 x^{17} - 82 x^{15} - 27 x^{11} + 7 x^{8} + 14 " src="/equation_images/%20f%28x%29%20%3D%20-%2016%20x%5E%7B19%7D%20-%2014%20x%5E%7B18%7D%20-%208%20x%5E%7B17%7D%20-%2082%20x%5E%7B15%7D%20-%2027%20x%5E%7B11%7D%20%2B%207%20x%5E%7B8%7D%20%2B%2014%20" alt="LaTeX: f(x) = - 16 x^{19} - 14 x^{18} - 8 x^{17} - 82 x^{15} - 27 x^{11} + 7 x^{8} + 14 " data-equation-content=" f(x) = - 16 x^{19} - 14 x^{18} - 8 x^{17} - 82 x^{15} - 27 x^{11} + 7 x^{8} + 14 " /> </p> </p><p> <p>The coefficient is <img class="equation_image" title=" \displaystyle a_n=-16 " src="/equation_images/%20%5Cdisplaystyle%20a_n%3D-16%20" alt="LaTeX: \displaystyle a_n=-16 " data-equation-content=" \displaystyle a_n=-16 " /> and is negative. The degree is <img class="equation_image" title=" \displaystyle 19 " src="/equation_images/%20%5Cdisplaystyle%2019%20" alt="LaTeX: \displaystyle 19 " data-equation-content=" \displaystyle 19 " /> and is odd. So the end behavior is
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