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Use translations, reflections, and stretches to graph \(\displaystyle f(x) = 6 e^{x + 7} + 1\). State the horizontal asymptote and the range of \(\displaystyle f(x)\).
The graph is shifted left 7 units and up 1 unit. The graph is stretched by a factor of 6 and the horizontal asymptote is \(\displaystyle y = 1\). The range is \(\displaystyle (1, \infty)\)
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\begin{question}Use translations, reflections, and stretches to graph $f(x) = 6 e^{x + 7} + 1$. State the horizontal asymptote and the range of $f(x)$.\newline
\soln{11cm}{The graph is shifted left 7 units and up 1 unit. The graph is stretched by a factor of 6 and the horizontal asymptote is $y = 1$. The range is $(1, \infty)$\newline
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\draw[very thick, latex-latex, color=blue, samples = 200, domain=-10:-6.6] plot ({\x}, {6*exp(\x + 7) + 1});
\draw[thick, dashed] (-10, 1) -- (10, 1);
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}
\end{question}
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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>Use translations, reflections, and stretches to graph <img class="equation_image" title=" \displaystyle f(x) = 6 e^{x + 7} + 1 " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%20%3D%206%20e%5E%7Bx%20%2B%207%7D%20%2B%201%20" alt="LaTeX: \displaystyle f(x) = 6 e^{x + 7} + 1 " data-equation-content=" \displaystyle f(x) = 6 e^{x + 7} + 1 " /> . State the horizontal asymptote and the range of <img class="equation_image" title=" \displaystyle f(x) " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%20" alt="LaTeX: \displaystyle f(x) " data-equation-content=" \displaystyle f(x) " /> .<br> </p> </p><p> <p>The graph is shifted left 7 units and up 1 unit. The graph is stretched by a factor of 6 and the horizontal asymptote is <img class="equation_image" title=" \displaystyle y = 1 " src="/equation_images/%20%5Cdisplaystyle%20y%20%3D%201%20" alt="LaTeX: \displaystyle y = 1 " data-equation-content=" \displaystyle y = 1 " /> . The range is <img class="equation_image" title=" \displaystyle (1, \infty) " src="/equation_images/%20%5Cdisplaystyle%20%281%2C%20%5Cinfty%29%20" alt="LaTeX: \displaystyle (1, \infty) " data-equation-content=" \displaystyle (1, \infty) " /> <br>
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