Question

What is the midline of this function? y=  

Answer 1

Answer:

Midline is at y = 0

Amplitude is; A = 1.5

g(a) = 1.5 sin 0.5x

Period = 4π

Max value; y = 1.5

Min value; y = -1.5

Step-by-step explanation:

From the graph, we know that amplitude is highest point of the graph which is 1.5.

Thus, A = 1.5

Now,period from the graph is distance between where the graph repeats which in this case is 2π + 2π = 4π

Now, equation of this curve is;

y = A sin(B(x + C)) + D

Where;

A is amplitude

B is 2π/period = 2π/4π = ½

C is phase shift

D is vertical shift

The function g(a) that will represent the behavior of the graphed function would be gotten by Plugging in the relevant values but in this case, there are no phase shifts or vertical shifts. Thus, C = D = 0

g(a) = 1.5 sin 0.5x

Midline is the point between the maximum and minimum values.

Max value is at y = 1.5

Min value is at y = -1.5

Midline of both from the graph is at x = -π/2 which is at y = 0