math

State the period, amplitude, max/min values, range, domain, horizontal phase shift and vertical displacement.
y = -3cos (2x - 30°) + 1

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  1. y = -3cos (2x - 30°) + 1
    y = -3cos (2(x - 15°)) + 1

    compare this y = a cos(k(𝝷 + d) + c
    where
    a is the amplitude
    period = 2π/k
    d is a horizontal phase shift of d units to the left ( for -d , the shift is to the right)
    c is the vertical displacement.
    for the max/min values, range, domain, you should be able to find these from the above information.
    Let me know what your answers are.

  2. -3: amplitude = 3
    cos (2x - 30°): period = 360/2 = 180°
    +1: vertical shift = up 1
    max/min of cos are ±1, so with our amplitude and vertical displacement, max/min = (0+1)±3 = 4,-2
    range is [min,max] = [-2,4]
    domain is all real numbers, as always
    cos(2x-30°) = cos(2(x-15°)) so horizontal displacement is 15° to the right

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