anonymous
  • anonymous
please help been stuck forever medal and fan For f(x) = x2 and g(x) = (x − 4)2, in which direction and by how many units should f(x) be shifted to obtain g(x)?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
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jdoe0001
  • jdoe0001
\(\bf f(x)=x^2\implies f(x)=(x+{\color{red}{ 0}})^2 \\ \quad \\ \quad \\ \textit{function transformations} \\ \quad \\ \begin{array}{llll} \begin{array}{llll} shrink\ or\\ expand\\ by\ {\color{purple}{ A}}\end{array} \qquad \begin{array}{llll} vertical\\ shift\\ by \ {\color{green}{ D}} \end{array} \begin{array}{llll}{\color{green}{ D}} > 0& Upwards\\ {\color{green}{ D}} < 0 & Downwards\end{array} \\ % template start \qquad \downarrow\qquad\qquad\quad\ \downarrow\\ g(x) = {\color{purple}{ A}} ( x {\color{red}{- 4}} ) + {\color{green}{ D}}\\ %template end \qquad\qquad \quad \uparrow \\ \qquad\begin{array}{llll} horizontal\\ shift\\ by \ {\color{red}{ C}}\end{array} \begin{array}{llll}{\color{red}{ C}} > 0 & to\ the\ left\\ {\color{red}{ C}} < 0& to\ the\ right\end{array} \end{array}\) what do you think?
anonymous
  • anonymous
plug in values into (x-4)^2 what do u notice

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anonymous
  • anonymous
Ok you should shift f(x) 4 places to the left
triciaal
  • triciaal
anonymous
  • anonymous
sorry im back im kind of lost
anonymous
  • anonymous
I mean to the right sorry
anonymous
  • anonymous
jdoe0001
  • jdoe0001
\(f(x)=x^2\implies f(x)=(x+{\color{red}{ 0}})^2 \\ \quad \\ \quad \\ \textit{function transformations} \\ \quad \\ \begin{array}{llll} \begin{array}{llll} shrink\ or\\ expand\\ by\ {\color{purple}{ A}}\end{array} \qquad \begin{array}{llll} vertical\\ shift\\ by \ {\color{green}{ D}} \end{array} \begin{array}{llll}{\color{green}{ D}} > 0& Upwards\\ {\color{green}{ D}} < 0 & Downwards\end{array} \\ % template start \qquad \downarrow\qquad\qquad\quad\ \downarrow\\ g(x) = {\color{purple}{ A}} ( x {\color{red}{- 4}} ) + {\color{green}{ D}}\\ %template end \qquad\qquad \quad \uparrow \\ \qquad\begin{array}{llll} horizontal\\ shift\\ by \ {\color{red}{ C}}\end{array} \begin{array}{llll}{\color{red}{ C}} > 0 & to\ the\ left\\ {\color{red}{ C}} < 0& to\ the\ right\end{array} \end{array}\) notice the function transformation for g(x), only "C" is changing from the original
anonymous
  • anonymous
ok so its c?
anonymous
  • anonymous
hold on
jdoe0001
  • jdoe0001
well. from the template, is the only value added notice, the difference from the "parent" function f(x) to g(x)
anonymous
  • anonymous
ok yes
jdoe0001
  • jdoe0001
so it has a horizontal shift, of 4 units the 4 is negative, meaning the horizontal shift is to the right http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4XjIiLCJjb2xvciI6IiMzQjE3RUQifSx7InR5cGUiOjAsImVxIjoiKHgtNCleMiIsImNvbG9yIjoiI0VEMEUwRSJ9LHsidHlwZSI6MTAwMH1d
anonymous
  • anonymous
ok yes

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