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What is the midline equation of the function $g(x)= 3\sin(2x-1)+4$

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Domain and range of square root functions: equations

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Q. What is the midline equation of the function

g(x)= 3\sin(2x-1)+4

Identify Vertical Shift: The midline of a sinusoidal function like $g(x) = 3\sin(2x-1) + 4$ is the horizontal line that represents the average value of the maximum and minimum values of the function. To find the midline, we need to identify the vertical shift of the function.
General Form of Sinusoidal Function: The general form of a sinusoidal function is $y = A\sin(Bx - C) + D$ , where $A$ is the amplitude, $B$ affects the period, $C$ is the phase shift, and $D$ is the vertical shift. The vertical shift, $D$ , determines the midline of the function.
Vertical Shift Analysis: In the given function $g(x) = 3\sin(2x-1) + 4$ , the coefficient $D$ is $4$ . This means that the vertical shift of the function is $4$ units upwards. Therefore, the midline is a horizontal line at $y = 4$ .
Midline Equation: The equation of the midline is simply $y = D$ , where $D$ is the vertical shift. So for $g(x) = 3\sin(2x-1) + 4$ , the midline equation is $y = 4$ .

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