use the graph to identify the amplitude for each function shown. the amplitude of the function shown in…

Explanation:

Step1: Recall amplitude definition

The amplitude of a periodic - function (y = A\sin(Bx - C)+D) or (y = A\cos(Bx - C)+D) is given by (|A|), and geometrically, it is half the vertical distance between the maximum and minimum values of the function.

Step2: Analyze orange - function

For the orange function, the maximum value is (y = 6) and the minimum value is (y=-6). The vertical distance between the maximum and minimum is (6 - (-6)=12). So the amplitude (A_1=\frac{12}{2}=6).

Step3: Analyze blue - function

For the blue function, the maximum value is (y = 2) and the minimum value is (y=-2). The vertical distance between the maximum and minimum is (2-(-2) = 4). So the amplitude (A_2=\frac{4}{2}=2).

Step4: Analyze green - function

For the green function, the maximum value is (y = 2) and the minimum value is (y=-2). The vertical distance between the maximum and minimum is (2-(-2)=4). So the amplitude (A_3=\frac{4}{2}=2).

Answer:

The amplitude of the function shown in orange is 6. The amplitude of the function shown in blue is 2. The amplitude of the function shown in green is 2.