What are the amplitude, period, and midline of the function? a)amplitude: 8; period: π; midline: y = 1 b)amplitude: 8; period: 2π; midline: y = 5 c)amplitude: 4; period: 2π; midline: y = 5 d)amplitude: 2; period: π; midline: y = 1

The answer is choice D
Amplitude: 2
Period: pi
Midline: y = 1



Explanation:

The largest y value possible is y = 3
The smallest y value possible is y = -1
Subtract and use absolute value to find the distance between the min and max
|Max - Min| = |3 - (-1)| = |3+1| = |4| = 4
Take half of this distance to get: 4/2 = 2
The amplitude is 2 units. This is the vertical distance from the midline to either the min or max.

Place a point at (0,-1) on the blue curve. If you move the point along the curve to the right, you'll move up and then move back down until you reach the point (pi,-1). Note how we moved pi units to the right. Once we reach this location, we repeat the cycle again. This process continues forever to generate the sine curve. Therefore, the period is pi units.

The largest y value possible is y = 3
The smallest y value possible is y = -1
The midpoint is found by adding up those values and dividing by 2:
(Max+Min)/2 = (3+(-1))/2 = 2/2 = 1
That's why the midline is y = 1

The answer is option c.