Answer:
y = -2sin(2x)
Explanation:
You are being asked to find the values of 'a' and 'b' that will make y = a·sin(bx) be the equation of the graph.
Parameters
In the equation y = a·sin(bx), the value 'a' determines the peak value of the graph. In the graph show, the maximum is 2, and the minimum is -2. This tells you the magnitude of 'a' is 2.
You know the graph of the sine function starts at (0, 0) and increases as x gets larger. Here, the graph starts at (0, 0) and decreases toward -2 as x gets larger. This tells you the sine function has been reflected over the x-axis, and that the sign of 'a' will be negative:
a = -2
The value 'b' determines the period of the graph. This graph contains one full cycle of the sine function as x goes from 0 to π, and then it repeats. That is, the period is π.
The period is related to b by the relation ...
b = 2π/P . . . . where P is the period
For P=π, this means ...
b = 2π/π = 2
The equation you want is y = -2·sin(2x).
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Additional comment
Since the graph does not exist outside the interval [0, 2π], we conclude that will be the domain of the function we have defined.
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