y = 4-2cos (πx - 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.
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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