Posted by **Emily ** on Thursday, August 22, 2013 at 4:06pm.

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 -
**Reiny**, Thursday, August 22, 2013 at 5:14pm
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

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