Answer:
Amplitude = 2
Period = [tex]2\pi[/tex]
midline: Â y = -2
y-intercept is (0, -2)
Step-by-step explanation:
[tex]f(x) = A sin(B(x + C)) + D[/tex]
- Amplitude = A
- Period =[tex]\dfrac{2\pi}{B}[/tex]
- Phase shift = C (positive is to the left)
- Vertical shift = D
For [tex]f(x)=2sin(x)-2[/tex]
- Amplitude = 2
- Period = [tex]2\pi[/tex]
- Phase shift = 0
- Vertical shift = -2
Midline is the midway point along the vertical distance of y between the max and min values of y
as  -1 ≤ sin(x) ≤ 1
⇒ max value when sin(x) = 1 ⇒ f(x) = 2 x 1 - 2 = 0
⇒ min value when sin(x) = -1 ⇒ f(x) = 2 x -1 - 2 = -4
Therefore, midline is y = -2
y-intercept is when x = 0
f(0) = 2 sin(0) -2 = 0 - 2 = -2
Therefore, y-intercept is (0, -2)
