Question

State the period, amplitude, max/min values, range, domain, horizontal phase shift and vertical displacement.
y = -3cos (2x - 30°) + 1

Answer 1

y = -3cos (2x - 30°) + 1
y = -3cos (2(x - 15°)) + 1

compare this y = a cos(k(𝝷 + d) + c
where
a is the amplitude
period = 2π/k
d is a horizontal phase shift of d units to the left ( for -d , the shift is to the right)
c is the vertical displacement.
for the max/min values, range, domain, you should be able to find these from the above information.
Let me know what your answers are.

Answer 2

-3: amplitude = 3
cos (2x - 30°): period = 360/2 = 180°
+1: vertical shift = up 1
max/min of cos are ±1, so with our amplitude and vertical displacement, max/min = (0+1)±3 = 4,-2
range is [min,max] = [-2,4]
domain is all real numbers, as always
cos(2x-30°) = cos(2(x-15°)) so horizontal displacement is 15° to the right