The graph appears to be a sinusoidal function, likely a sine or cosine function, given its periodic nature and the presence of maximum and minimum points.
The maximum value of the function is 8 and the minimum value is -8. The amplitude AAA is half the distance between the maximum and minimum values: A=8−(−8)2=8 A = \frac{8 - (-8)}{2} = 8 A=28−(−8)=8
The period TTT is the distance between two consecutive points where the function repeats its pattern. From the graph, the function repeats every 2π2\pi2π units along the x-axis.
The function is of the form y=Asin(Bx) y = A \sin(Bx) y=Asin(Bx) or y=Acos(Bx) y = A \cos(Bx) y=Acos(Bx). Given the amplitude A=8A = 8A=8 and the period T=2πT = 2\piT=2π, we have B=2πT=1B = \frac{2\pi}{T} = 1B=T2π=1. Therefore, the function can be written as: y=8sin(x) y = 8 \sin(x) y=8sin(x) or y=8cos(x) y = 8 \cos(x) y=8cos(x).
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