Question

someone please help man ? anyone

Answer 1

Answer:

f(x) = 2 sin ( 2π x / 3 )  +  5

Step-by-step explanation:

The sinusoidal function has the form:

f(x) = A sin ( 2π ( x - b ) / p )  +  C

where:

• A is the amplitude
• b is the horizontal shift
• p is the period
• C is the vertical shift / position of the midline

The midline is through the point (0, 5), so C = 5.

The x-coordinate here is 0 so there is no horizontal shift; i.e. b = 0.

The maximum has y-coordinate 7, which is 7-5=2 above the midline, so the amplitude is 2.  i.e. A=2

The function goes from the midline to the maximum over a horizontal distance of 0.75 - 0 = 0.75.  This is one quarter of the period (the whole period goes midline -> maximum -> midline -> minimum -> midline).  So the period is p = 4×0.75 = 3.

Putting these together:

f(x) = 2 sin ( 2π x / 3 )  +  5