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# Graph the function: f(x)=-4cos(2/3x+pi/3)-3

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Graph the function: f(x)=-4cos(2/3x+pi/3)-3

Be sure to show the calculation for the period, phase shift, midline, and amplitude, and clearly label the axes and graph at least one full period of the function.

Mar 14, 2023

#1
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It is easiest if it is of the form

$$f(x)=Acos[b(x-p)]+M$$

A is the amplitude (if neg then it is upside down)

2pi/b  is the period

y=M is the midline

p is the phase schift

Now I think of it in bits, sketch it as you go. So that you build up the graph step by step

consider

$$1) y=cos(x)\\ 2) y=-cos(x)\\ 3) \text{make the numbers on the x axis fit with a period of } 2\pi/b\\ 4) \text{drop or raise the graph so the centre line is }y=M\\ \\5) \text{Change the amplitude by making the bottom of the wave M-A and the top M+A }\\ 6) \text{Shift the phase by p units to the right}$$

f(x)=-4cos(2/3x+pi/3)-3

Mar 15, 2023