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Questions: Algebra BusinessCalculus
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Find the domain and range of \(\displaystyle f(x)=4 \left(x + 1\right)^{2} + 6 \)
The domain of every polynomial is all real numbers. The sign of \(\displaystyle a\) is positive so the function has a minimum value at the vertex. This gives the range as \(\displaystyle [6,\infty)\)
\begin{question}Find the domain and range of $f(x)=4 \left(x + 1\right)^{2} + 6 $
\soln{9cm}{The domain of every polynomial is all real numbers. The sign of $a$ is positive so the function has a minimum value at the vertex. This gives the range as $[6,\infty)$}
\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>Find the domain and range of <img class="equation_image" title=" \displaystyle f(x)=4 \left(x + 1\right)^{2} + 6 " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%3D4%20%5Cleft%28x%20%2B%201%5Cright%29%5E%7B2%7D%20%2B%206%20%20" alt="LaTeX: \displaystyle f(x)=4 \left(x + 1\right)^{2} + 6 " data-equation-content=" \displaystyle f(x)=4 \left(x + 1\right)^{2} + 6 " /> </p> </p><p> <p>The domain of every polynomial is all real numbers. The sign of <img class="equation_image" title=" \displaystyle a " src="/equation_images/%20%5Cdisplaystyle%20a%20" alt="LaTeX: \displaystyle a " data-equation-content=" \displaystyle a " /> is positive so the function has a minimum value at the vertex. This gives the range as <img class="equation_image" title=" \displaystyle [6,\infty) " src="/equation_images/%20%5Cdisplaystyle%20%5B6%2C%5Cinfty%29%20" alt="LaTeX: \displaystyle [6,\infty) " data-equation-content=" \displaystyle [6,\infty) " /> </p> </p>