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What is the midline equation of the function

{:[g(x)=2cos(7x+5)+1?],[y=◻]:}

What is the midline equation of the function\newlineg(x)=2cos(7x+5)+1?y= \begin{array}{l} g(x)=2 \cos (7 x+5)+1 ? \\ y=\square \end{array}

Full solution

Q. What is the midline equation of the function\newlineg(x)=2cos(7x+5)+1?y= \begin{array}{l} g(x)=2 \cos (7 x+5)+1 ? \\ y=\square \end{array}
  1. Identify Midline: The midline of a trigonometric function like g(x)=2cos(7x+5)+1g(x) = 2\cos(7x+5) + 1 is the horizontal line that represents the average value of the function over one period. It is the value that the function oscillates around. To find the midline, we look at the vertical shift of the function, which is given by the constant term outside the cosine function.
  2. Determine Vertical Shift: In the given function g(x)=2cos(7x+5)+1g(x) = 2\cos(7x+5) + 1, the vertical shift is +1+1. This means that the midline is a horizontal line at y=1y = 1.
  3. Calculate Midline Equation: Therefore, the equation of the midline is simply y=1y = 1.

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