## anonymous one year ago 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)?

1. anonymous

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2. 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?

3. anonymous

plug in values into (x-4)^2 what do u notice

4. anonymous

Ok you should shift f(x) 4 places to the left

5. triciaal

@joyraheb no

6. anonymous

sorry im back im kind of lost

7. anonymous

I mean to the right sorry

8. anonymous

Thx @triciaal

9. 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

10. anonymous

ok so its c?

11. anonymous

hold on

12. jdoe0001

well. from the template, is the only value added notice, the difference from the "parent" function f(x) to g(x)

13. anonymous

ok yes

14. 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

15. anonymous

ok yes