name:____ date:____ pd:____ key features of sinusoidal functions practice 1) equation of the midline:____…

Explanation:

Step1: Find mid - line for first graph

The mid - line is the horizontal line halfway between the maximum and minimum values. For the first graph, the maximum is around (y = 1) and the minimum is around (y=-3). The mid - line is (y=\frac{1+( - 3)}{2}=-1).

Step2: Calculate amplitude for first graph

The amplitude (a) is the distance from the mid - line to the maximum or minimum. For the first graph, with mid - line (y = - 1) and maximum (y = 1), (a=\vert1-( - 1)\vert = 2). Here (d=-1) (the value of the mid - line).

Step3: Write equation of sinusoid for first graph

The general form of a sinusoid is (y = a\sin(bx - c)+d). Assuming (b = 1) and (c = 0) (since no phase shift information is given from the graph), the equation is (y = 2\sin(x)-1).

Step4: Find mid - line for second graph

The maximum is around (y = 7) and the minimum is around (y=-1). The mid - line is (y=\frac{7+( - 1)}{2}=3).

Step5: Calculate amplitude for second graph

With mid - line (y = 3) and maximum (y = 7), (a=\vert7 - 3\vert=4). Here (d = 3).

Step6: Write equation of sinusoid for second graph

Assuming (b = 1) and (c = 0), the equation is (y=4\sin(x)+3).

Equation of the midline: (y=-1) Amplitude: (2) (a = 2) (d=-1) Equation of Sinusoid: (y = 2\sin(x)-1)

Equation of the midline: (y = 3) Amplitude: (4) (a = 4) (d = 3) Equation of Sinusoid: (y=4\sin(x)+3)