What are the amplitude, period, and midline of the function? (0,1), (pi/2,-5), (pi, 1), (3*pi/2,-5), (2pi, 1)

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Mathematics

Eddie Johnston

13 January, 04:51

What are the amplitude, period, and midline of the function? (0,1), (pi/2,-5), (pi, 1), (3*pi/2,-5), (2pi, 1)

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Garrett Elliott · Answer 1

The period is pi, since this is how often a value of 1 repeats (at x = 0, x = pi, and x = 2pi).

The range of the function is from - 5 to 1, so this is a distance of 6 units, and the amplitude is 6/2 = 3 units.

The midline of the function is determined by taking the average of the maximum and minimum values: (-5 + 1) / 2 = - 2. Therefore, the midline is at y = - 2.