Answer:
The sin function is [tex]y=3 sin(\frac{1}{2}x)+2[/tex]
Maximum point is [tex](\pi,5)[/tex]
Step-by-step explanation:
Given : A sine function whose amplitude is 3, period is [tex]4\pi[/tex], midline is y=2, and y-intercept is (0,2). The graph is not a reflection of the parent function over the x-axis.
To plot the graph :
Solution :
General form of sin function is [tex]y=A sin(Bx)+C[/tex]
Where A is the amplitude
[tex]B=\frac{2\pi}{\text{Period}}[/tex]
C is the midline
Substitute the given key features
A=3 , C=2
[tex]B=\frac{2\pi}{4\pi}=\frac{1}{2}[/tex]
The function is not a reflection of its parent function over the x-axis.
The sin function is [tex]y=3 sin(\frac{1}{2}x)+2[/tex]
Now, We plot the graph of the sin function.
The graph is attached below.
First point is midline i.e, (0,2)
Maximum point is [tex](\pi,5)[/tex]
