y = 4-2cos (**π****x - 4)**

I know its parent graph would be y= 4-2cos **πx after i factor πx out but i dont know what to say for the period. if its 4/pi how do how do i graph it.**

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The graph of `y=4-2cos(pix-4)` :

The base graph is `y=cosx`

The transformations given by `y=acosb(x-h)+k` are as follows:

(a) changes the amplitude (vertical stretch/compression) and if a<0 it reflects across the horizontal axis.

(b) affects the period (horizontal stretch/compression) The period is given by `p=(2pi)/b`

(h) is a horizontal translation of h units

(k) is a vertical translation of k units (shifts the midline up/down)

So we have `y=-2cospi(x-4/pi)+4`

The amplitude is 2; the graph is reflected over the horizontal axis.

The period is `p=(2pi)/pi=2`

The graph is translated `4/pi` units to the right

The graph is translated 4 units up (The midline will be y=4)

The graph of `y=cosx` in black; ampliitude and reflection (`y=-2cosx`) in purple; period change (`y=-2cospix`) in blue; horizontal shift (phase shift) in green and final transformation vertical translation in red.

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