Understanding Trig Function Behavior: Period, Amplitude, and Shifts

[aisha]

Hi just need a little help with the behaviour of this trig function

$$y=-3\cos (2x-\frac {\pi} {6}) +1$$
I converted the pi over 6 to degrees and got -30

need to state the period, amplitude, max/min values, range, domain, horizontal phase shift, and vertical dispacement.

So far after rearranging the the equation i have

period= $$pi$$
range= ?
amplitude=?
domain= all values XER
horizontal phase shift= 15 degrees left
vertical displacement= up 1
max\min ? not sure how to figure this out from the equation i tried graphing using the graphing calculator but it won't give me the values for max and min. Therefore I cannot solve for amplitude yet and same with range.

CAN SOMEONE PLEASE HELP ME JUST NEED HELP WITH THE MAX AND MIN THANKS

 

[aisha]

I got
max = 4, min = -2
amplitude = 3
range = {y:-2 <= y <= 4}

is this correct or have i done something wrong..please check and reply soon!

 

[Fermat]

what are the max and min values of the cos function?
Use that to figure out the max and min values of y.

 

[Fermat]

I got
max = 4, min = -2
amplitude = 3
range = {y:-2 <= y <= 4}

is this correct or have i done something wrong..please check and reply soon!

yes, those are correct.

 

[aisha]

is everything else correct too the period domain and shifts?

 

[Fermat]

Yes - everything else looks ok.