Answer:
Required equation of midline is x=4.
Step-by-step explanation:
Given function is,
[tex]g(x)=3\sin (2x-1)+4\hfill (1)[/tex]
In standerd form (1) can be written as,
[tex]a\sin (bx+c)\pm d[/tex]
where,
|a|= amplitude.
b= vertical shift.
c= horizontal shift.
Midline is the line which runs between maximum and minimum value.
In this problem,
a=3, b=2, c=-1, d=4
So amplitude a=3 and graph is shifted 4 units in positive y-axis.
Therefore,
Maximum value = d + a = 4 + 3 = 7
Minumum value = d - a = 4 - 3 = 1
Midline will be centered of the region (7, 1) that is at 4.
Hence equation of midline is x=4.
