+20 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.
+118677
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
