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

 

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