A sine function has the following key features: Period = 4 Amplitude = 3 Midline: y=−1 y-intercept: (0,-1) The function is not a reflection of its parent function over the x-axis. Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.

See the graphs attached and the explanation below

Explanation:

The most simple sine function, considered the parent function, is:

     

That function has:

Midline, also known as rest or equilibrium position: y = 0Minimum: - 1Maximum: 1Amplitude: the distance between a minimum or a maximum and the midline = 1period: the interval of repetition of the function = 2π

The more general sine function is:

             

That function has:

Midline: y = D (it is a vertical shift from the parent function)Minimum: - A + DMaximum: A + DAmplitude: Aperiod: 2π/Bphase shift: C (it is a horizontal shift of the from the parent function)

Now, you have to draw the sine function with the given key features:

Period = 4 ⇒ 2π/B = 4 ⇒ B = π/2Amplitude, A = 3midline y = - 1 ⇒ D = - 1y-intercept = (0, -1)

Substitute the know values and use the y-intercept to find C:

       

           

Substitute (0, -1)

             

             

Hence, the function to graph is:

             

To draw that function use this:

Maxima: 3(1) - 1 = 3 - 1 = 2, at x = 1 ± 4n (n = 0, 1, 2, 3, ...)Minima: 3(-1) - 1 = - 3 - 1 = -4y-intercept: (0, - 1)x-intercepts: the solutions to 0 = 3sin(πx/2) = - 1first point of the midline: (0, -1) it is the same y-intercept

With that you can understand the graphs attached.