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

Question

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

Answer 1

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