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Math

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1) What is the amplitude, period, horizontal shift (relative to basic function), and vertical translation of the following: a) -3cos(x+ 3.14/4) and b) 2sin(x-3.14/2)+3
2) evaluate the following expressions: a) log2 cubed root of 16 b) log25 (1/125) c) e^2ln5 d) ln 1/the cubed root of e^5

  • Math -

    I will do 1 b) you do a)

    y = 2 sin (x - π/2) + 3
    amplitude = 2
    period = 2π
    phase shift = π/2 to the right
    vertical translation : 3 units up

    2. a) log216^(1/3)
    = log2(2^4)^(1/3)
    = log22^(4/3)
    = (4/3) log2 2
    = 4/3

    b) log25 1/125
    = log251 - log25125
    = 0 - log25 25^(3/2)
    = -3/2

    c) e^2ln5
    = e^(ln 5^2))
    = 5^2 = 25 , based on property that e^lnk = k

    d) ln (1/( e^5)^(1/3)
    = ln1 - ln e^(5/3)
    = 0 - 5/3 lne
    = -5/3

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