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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.

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  1. anonymous
    • one year ago
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    i am here to save the day!

  2. a1234
    • one year ago
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    ok...

  3. anonymous
    • one year ago
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    lol just kidding i have no idea how to solve this @mitchal

  4. anonymous
    • one year ago
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    @Preetha @Nnesha @kiamousekia @nevermind_justschool

  5. anonymous
    • one year ago
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    b isn't true. f and g have the same period

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

  7. anonymous
    • one year ago
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    y = a cos b(x - c)) + d a = amplitude b = (2π)/period c = phase shift d = vertical shift

  8. a1234
    • one year ago
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    Is it c? But then what's the difference between c and a?

  9. anonymous
    • one year ago
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    Hmmm 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

  10. anonymous
    • one year ago
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    And 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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