2 Answers:
=====================================================
Explanation:
Let's go through the answer choices
---------------------------------
A)
The lowest point is y = 1, and the highest point is y = 27. Computing the midpoint gets us (yMin+yMax)/2 = (1+27)/2 = 28/2 = 14.
The midline of is y = 14.
Consider that the parent function has a midline of y = 0. The jump from y = 0 to y = 14 must mean has a vertical shift of 14.
Choice A is true
---------------------------------
B)
The period is the length of the cycle. For the function , the function starts at and repeats when it gets to . This is a difference of pi/2 units which is the period.
Choice B is false. It contradicts with choice E.
---------------------------------
C)
Choice C is false. The max for is at y = 27
---------------------------------
D)
To figure out the amplitude, we can note the vertical distance from the midline y = 14 to the max is 27-14 = 13 units.
Or we can note the distance from the midline to the min is 14-1 = 13 units.
Or we subtract the min and max, and divide by 2: (yMax-yMin)/2 = (27-1)/2 = 26/2 = 13
Either way, the amplitude is 13 units
Choice D is false.
---------------------------------
E)
Choice E is true. Refer to choice B to see why this is the case.
---------------------------------
Side note: one possible function is . The various pieces of that function (in)directly lead to the amplitude, period, and vertical shift.