Answer :
Answer:
The sin function is [tex]y=6sin(\frac{1}{4}x)+3[/tex]
Step-by-step explanation:
Given : A sine function has the following key features:
Frequency = [tex]\frac{1}{8\pi}[/tex], Amplitude = 6, Midline: y = 3, y-intercept: (0,3)
The function is not a reflection of its 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=6 , C=3
Period= 1/Frequency
[tex]P=8\pi[/tex]
[tex]B=\frac{2\pi}{8\pi}=\frac{1}{4}[/tex]
The sin function is [tex]y=6sin(\frac{1}{4}x)+3[/tex]
The function is not a reflection of its parent function over the x-axis.
The sin function is [tex]y=6 sin(\frac{1}{4}x)+3[/tex]
The graph is attached below.
