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a1234
 one year ago
Describe the relationships between the graphs of f and g. Think about amplitudes, periods, and shifts.
f(x) = cos4x
g(x) = 2 + cos4x
a. g(x) is 2 units down compared to f(x).
b. The period of g(x) is twice of that of f(x).
c. g(x) is a vertical shift of 2 units downward.
a1234
 one year ago
Describe the relationships between the graphs of f and g. Think about amplitudes, periods, and shifts. f(x) = cos4x g(x) = 2 + cos4x a. g(x) is 2 units down compared to f(x). b. The period of g(x) is twice of that of f(x). c. g(x) is a vertical shift of 2 units downward.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i am here to save the day!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lol just kidding i have no idea how to solve this @mitchal

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Preetha @Nnesha @kiamousekia @nevermind_justschool

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0b isn't true. f and g have the same period

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1\(\textit{function transformations} \\ \quad \\ \begin{array}{llll} \begin{array}{llll} shrink\ or\\ expand\\ by\ {\color{purple}{ A}}\cdot {\color{blue}{ B}}\end{array} \qquad \begin{array}{llll} vertical\\ shift\\ by \ {\color{green}{ D}} \end{array} \begin{array}{llll}{\color{green}{ D}} > 0& Upwards \\ \quad \\ {\color{green}{ D}} < 0 & Downwards\end{array} \\ \qquad \downarrow\qquad\qquad\quad\ \downarrow\\ % template start f(x) = {\color{purple}{ A}} ( {\color{blue}{ B}}x + {\color{red}{ C}} ) + {\color{green}{ D}}\\ % template ends \qquad\qquad\quad\ \uparrow \\ \qquad\begin{array}{llll} horizontal\\ shift\\ by \ \frac{{\color{red}{ C}}}{{\color{blue}{ B}}}\end{array} \begin{array}{llll}\frac{{\color{red}{ C}}}{{\color{blue}{ B}}} > 0 & to\ the\ left \\ \quad \\ \frac{{\color{red}{ C}}}{{\color{blue}{ B}}} < 0& to\ the\ right\end{array} \end{array}\\ \\ \bf f(x)=cos({\color{blue}{ 4}}x)\qquad \qquad g(x)=2+cos({\color{blue}{ 4}}x)\iff g(x)=cos({\color{blue}{ 4}}x){\color{green}{ 2}}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y = a cos b(x  c)) + d a = amplitude b = (2π)/period c = phase shift d = vertical shift

a1234
 one year ago
Best ResponseYou've already chosen the best response.0Is it c? But then what's the difference between c and a?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hmmm tricky question... my guess would be that it isn't c because they didnt specify what it was shifted down from. Presumably they mean the origin, but because they didn't say it is ambiguous whereas a specifies the magnitude of the shift and gives a reference from where the pellet occurs

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And since both amplitude and period are equal (with no phase difference) then at all points g(x) will be the exact same graph as f(x) only shifted downward by 2
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