Question

The manager recognizes that the data approximates a transformation of the parent sine function. Which value is closest to the midline of the transformed function?

a. 17
b. 20
c. 24
d. 14

Answer 1

The value closest to the midline of the transformed function is (c) 24.

Step-by-step explanation:

The midline of a sine function is determined by the vertical shift or translation. For a sine function in the form
`\(y = A \sin(B(x - C)) + D\)`, where Ais the amplitude, B is the frequency, C is the phase shift, and Dis the vertical shift, the midline is given by y = D.

In the provided question, the data approximates a transformation of the parent sine function, indicating a vertical shift. The transformed function's midline corresponds to the vertical shift, and in this case, it is the value of D. Comparing the options, the value closest to the midline is 24, making option (c) the correct choice.

To elaborate further, consider that a positive D shifts the graph upwards, while a negative D shifts it downwards. In this context, the midline is essentially the average or equilibrium level of the function. Thus, the answer is determined by the value that centers the sine function in the vertical direction. In the given options, 24 aligns closest to this central level, making it the most appropriate choice for the midline of the transformed function.

Therefore, based on the analysis of the sine function's transformation, the correct answer is option (c) 24, representing the value closest to the midline of the transformed function.