Answer:
graph 4 (reflected vertically)
Explanation:
You want the graph that represents a cosine function with no horizontal shift, an amplitude of 2, and a period of 2π/3.
Amplitude
The amplitude of a sine or cosine function is the difference between the positive peak and the centerline. All of the graphs show functions with an amplitude of 2.
Period/Frequency
The period of the function is the difference of x-values between the first instance of the function and the first repeat: f(x) ≡ f(x+p) has a period of p.
Graphs 1 and 3 show periods of 2π/9; graphs 2 and 4 show periods of 2π/3, as required.
Horizontal shift
There is an interaction between horizontal shift and vertical reflection. Sine or cosine functions are effectively inverted (reflected over the x-axis) if they are shifted horizontally by 1/2 period—and vice versa.
The function in graph 3 is a sine function, or a horizontally shifted cosine function.
The function in graph 4 is a cosine function that has been shifted 1/2 perior, OR a cosine function that has been reflected over the x-axis.
Graph 4 is the only viable choice for a cosine function with the correct period, so we have to assume it starts at -2 because it has been reflected vertically over the x-axis. (There seems to be no restriction on that in the problem statement.)
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Additional comment
Ordinarily, you might not be expected to make any assumptions about vertical reflection. It seems a bit of a trick question.