Answer:
[tex]f(x)=2\cos(x-\pi)-1[/tex]
Step-by-step explanation:
The general cosine function is given by
[tex]f(x)=A\cos(Bx-C)+D[/tex]
where [tex]A=2[/tex] is the amplitude,
[tex]Period=\frac{2\pi}{B}[/tex]
[tex]\Rightarrow 2\pi=\frac{2\pi}{B}[/tex]
[tex]\Rightarrow B=1[/tex],
[tex]c=\pi[/tex] is the horizontal shift and [tex]D=-1[/tex] is a downward vertical shift.
If we substitute all these values into the formula we obtain;
[tex]f(x)=2\cos(x-\pi)-1[/tex]
