Question

Consider the function

f(x)=-5cos((2/3)x-(pi/6))

a). Is there a reflection? Does the graph start at a maximum, a minimum, or an x-intercept?

For Amplitude I got 5

For Period I got 3pi

And for Phase shift I got 3pi/12 or => pi/4

Answer 1

yes, amplitude is five and period is 3 pi
when x = 0:

y = 5 cos (-pi/6) = 5 (.866)

that is not a max or a min or and x intercept

However there is always a reflection about the points where the argument of the cos function is zero because cos -z = cos z
that is when
(4/6)x = pi/6
or x = pi/4 which is 45 degrees
of course every time that argument increases or decreases by 2 pi (which is x increases or decreases by 3 pi as you said) you have another max and symmetry

Yes, (pi/6)/(2/3) = pi/4 = phase shift

see:
http://www.mathsisfun.com/algebra/amplitude-period-frequency-phase-shift.html