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28 December, 05:42

A cosine function has a period of 4, a maximum value of 20, and a minimum value of 0. The function is a not a reflection of its parent function over the x-axis.

Which function could be the function described?

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  1. 28 December, 07:24
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    Since the function is not a reflection over the x-axis we know that the maximum of 20 reached is due to a translation up and not an increase in amplitude.

    Basic form of a sinusoidal function: F (t) = A Cos (bt - c) + d

    |A| = amplitude, distance from max/min to center of the graph.

    b = frequency

    2π/b = period

    c = phase shift, shifts graph left/right

    d = vertical shift

    Given information:

    max = 20; min = 0 so the amplitude is 20/2, A = 10

    Center of the graph is then shifted up 10 units. d = 10

    period is 4 = 2π/b

    b = π/2

    * insert the values ...

    F (t) = 10 Cos (πt/2) + 10

    should look something like that. Maybe has a phase shift, c value or sine instead of cosine would still be a valid solution.
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