The function given has the following form:
[tex]y=A\cos (B(x+C))+D[/tex]
In this functions we have that:
• A is the amplitude.
,
• The period is 2pi/B
,
• Phase shift (horizontal translation) is C (to the left is C is positive.
,
• Vertical shift is D.
Now, we need to remember that the cosine function has a graph:
Now, in our function:
[tex]y=2\cos (x-\frac{\pi}{2})-1[/tex]
Comparing with the general cosine above we conclude that:
• The amplitude is 2.
,
• The phase shift is pi/2 to the right.
,
• The vertical shift is 1 down.
,
• The period is 2pi.
Then the graph is:
Comparing with the options we conclude that the answer is B.
