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A sine function has the following key features:

Frequency = 1/4π

Amplitude = 2

Midline: y = 2

y-intercept: (0, 2)

The function is not a reflection of its parent function over the x-axis.

Graph the function.

 Apr 10, 2019
 #1
avatar+111430 
+1

We have the form

 

y = Asin (Bx)  + C

 

A = the amplitude  = 2

 

Frequency  =  1 /period

 

1 / (4pi)  =  1 /period

 

So...the period = 4pi

 

So

 

B  =  2pi / [ period]   =   2pi / [ 4pi]  =  2 / 4    =  1 / 2

 

C = the shift up/down....since we have a y int of (0,2)....the normal sine function is shifted up 2 units....so C = 2

 

So....the function is

 

y = 2sin ( (1/2) x) + 2

 

Here is the graph :  https://www.desmos.com/calculator/zv9mibfgjv

 

 

cool  cool   cool

 Apr 10, 2019
edited by CPhill  Apr 10, 2019

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