Question

Please help me put with this problem

Answer 1

D. y = 3sin(1/2x)

Explanation:

You want to know the equation that corresponds to the graph.

Scaling

The graph shows one cycle of a sine function. It has a peak value of 3, indicating a vertical scaling by a factor of 3. All of the answer choices have this scale factor:

y = 3sin( )

That one cycle extends from x = -2π to x = 2π, a total of 2π -(-2π) = 4π units. The period of the parent sine function y=sin(x) is 2π, so this represents a horizontal expansion by a factor of 2. That scaling is represented in the function's equation as a divisor of x:

y = 3sin(x/2)

`\boxed{y=\sin{\left((1)/(2)x\right)}}`