Which transformations are needed to change the parent sine function to the sine function below? On a coordinate plane, a curve crosses the y-axis at y = 1.5. It has a minimum at y = 0.5 and a maximum at y = 1.5. It goes through one cycle at 4 pi. Vertical compression of One-half, horizontal stretch to a period of 4 pi, vertical shift of 1 unit up, phase shift of Pi units left vertical stretch of 2, horizontal compression to a period of 4 pi, vertical shift of 2 units up, phase shift of Pi units left vertical stretch of One-half, horizontal compression to a period of 2 pi, vertical shift of 1 unit up, phase shift of Pi units left vertical compression of One-half, horizontal stretch to a period of 2 pi, vertical shift of 1 unit down, phase shift of Pi units left
Question
Answer:
Vertical compression of One-half, horizontal stretch to a period of 4 pi, vertical shift of 1 unit up and a phase shift of pi units left
Step-by-step explanation:
The parameters of the sine function are;
The point the curve crosses the y-axis (at x = 0) = 1.5
The minimum of the curve is y = 0.5
The maximum is y = 1.5
The time it goes through one cycle = 4 pi
The general form of the sine function is presented as follows;
y = A·sin(B·(x – C)) + D
From the given information, we have;
A = 0.5
The period = 4·π = 2·π/B
∴ B = 1/2
At x = 0, y = max, therefore, B·(x – C) = (1/2)·(0 – C) = π/2
∴ C = -π
D = 1
Therefore, the given sine function can be presented as follows;
y = 0.5·sin((1/2)·(x – π)) + 1
Therefore, the transformation needed to change the parent sine function to the given sine function are
Vertical compression of One-half, horizontal stretch to a period of 4 pi, vertical shift of 1 unit up and a phase shift of pi units left