Answer :

we have the function

[tex]y=\frac{1}{2}cos(2x)-1[/tex]

Verify each statement

Option A

Find out the period

The period is

Period=2pi/B

The Period goes from one peak to the next

B=2

Period=2pi/2

Period=pi

so

Statement A is not true

Option B

Find out the amplitude

Looking at the equation

Amplitude=1/2

so

Statement B is not true

Option C

Find out the midline

midline=(-1.5-0.5)/2=-1

Statement C is true

Option D

The domain of the function is the interval (-infinite, infinite) (all real numbers)

Statement D is not true

therefore

The answer is option C

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