A sine function has the following key features:
- Frequency = 1/4π
- Amplitude = 2
- Midline: y = 2
The function is not a reflection of its parent function over the x-axis.We have to use the sine tool to graph the function.
The sin function : [tex]\rm y =-3\sin \left( \dfrac{x}{2} \right)+2[/tex]
Given:
- Frequency = 1/4π
- Amplitude = 2
- Midline: y = 2
- Period = 4π
- y-intercept: (0,2)
The function is the reflection of its parent function above the
x-axis.
According to the question, we know that
The General form of Sin function is [tex]\rm y =A\sin(Bx)+C[/tex]
Where,
A = Amplitude
B = [tex]\rm \dfrac {2\pi }{Period}[/tex]
C= Midline
Now we will substitute the features,
[tex]\rm A = 3\\\\ \rm B = \dfrac{2\pi }{4\pi }=\dfrac{1}{2}\\\\C=2[/tex]
Then,
The Sin function [tex]\rm y =-3\sin \left( \dfrac{x}{2} \right)+2[/tex]
According the given statement : The function is not a reflection of its parent function over the x-axis.We have to use the sine tool to graph the function.
Then, the coordinate will become (x,y)→(x,-y)
Now,
We plot the graph given below of the sin function
- First point is midline i.e, (0,2)
- Maximum point will be ( -π , 5 )
- Minimum point will be ( π , -1 )
Learn more about Sine functions here :https://brainly.com/question/9150949
