Math
posted by Emily on .
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(x3.14/2)+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

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) log_{2}16^(1/3)
= log_{2}(2^4)^(1/3)
= log_{2}2^(4/3)
= (4/3) log_{2} 2
= 4/3
b) log_{25} 1/125
= log_{25}1  log_{25}125
= 0  log_{25} 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