Answer:
A) y = 2; B) 3; C) 5; D) 1; E) 2π
Step-by-step explanation:
ƒ(x)=3sinθ + 2
In this function,
3= the amplitude, and
2 = the vertical shift
F) Graph
The figure below shows the graph of your function.
A) Equation of Midline
The midline is the horizontal line that passes through (0,2). Its equation is
ƒ(x) = 2
B) Amplitude
The amplitude is the maximum distance from the midline to the peak or the trough of a wave.
The peaks of your wave are at y = 5 (three units above the midline) and the troughs are at y = -1 (three units below the midline), so
Amplitude = 3
C) Maximum
The maxima are the largest y-values the function can reach (the peaks).
Max = 5
D) Minimum
The minima are the smallest y-values the function can reach (the troughs).
Min = -1
E) Period
The period is the length of one cycle of the curve. It is the distance between two peaks, two troughs, or two crossings of the midline.
Period = 2π ≈ 6.3
