## anonymous one year ago Functions f(x) and g(x) are shown below: f(x) g(x) f(x) = -4(x - 6)2 + 3 g(x) = 2 cos(2x - π) + 4 Using complete sentences, explain how to find the maximum value for each function and determine which function has the largest maximum y-value

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1. jdoe0001

have you covered function transformations yet? should be in your book

2. jdoe0001

$$\textit{function transformations} \\ \quad \\ \begin{array}{llll} \begin{array}{llll} shrink\ or\\ expand\\ by\ {\color{purple}{ A}}\end{array} \qquad \begin{array}{llll} vertical\\ shift\\ by \ {\color{green}{ D}} \end{array} \begin{array}{llll}{\color{green}{ D}} > 0& Upwards\\ {\color{green}{ D}} < 0 & Downwards\end{array} \\ % template start \qquad \downarrow\qquad\qquad\quad\ \downarrow\\ y = {\color{purple}{ -4}} ( x - {\color{red}{ 6}} )^2 + {\color{green}{ 3}}\\ %template end \qquad\qquad \quad \uparrow \\ \qquad\begin{array}{llll} horizontal\\ shift\\ by \ {\color{red}{ C}}\end{array} \begin{array}{llll}{\color{red}{ C}} > 0 & to\ the\ left\\ {\color{red}{ C}} < 0& to\ the\ right\end{array} \end{array} \\ \quad \\ -------------------------------------------- \\ \quad \\ \begin{array}{llll} \begin{array}{llll} shrink\ or\\ expand\\ by\ {\color{purple}{ A}}\end{array} \qquad \begin{array}{llll} vertical\\ shift\\ by \ {\color{green}{ D}} \end{array} \begin{array}{llll}{\color{green}{ D}} > 0& Upwards\\ {\color{green}{ D}} < 0 & Downwards\end{array} \\ % template start \qquad \downarrow\qquad\qquad\quad\ \downarrow\\ y = {\color{purple}{ 2}}cos ( {\color{blue}{ 2}} x - {\color{red}{ \pi }} ) + {\color{green}{ 4}}\\ %template end \qquad\qquad \quad \uparrow \\ \qquad\begin{array}{llll} horizontal\\ shift\\ by \ {\color{red}{ C}}\end{array} \begin{array}{llll}{\color{red}{ C}} > 0 & to\ the\ left\\ {\color{red}{ C}} < 0& to\ the\ right\end{array} \end{array}$$

3. jdoe0001

for the maximum y-value, the only transformation that matters are the vertical shift and in the g(x) case, the "amplitude", or A component

4. jdoe0001

well, for g(x) the "A"mplitude and the vertical shift, because the amplitude is a shift as well for trigonometric ones

5. anonymous

Try using the second derivative test