Answer:
[tex]y=A\sin(B(x+C))+D[/tex]
Amplitude = A
The height from the center line to the peak (or trough).
Period = (2π)/B
The horizontal distance from one peak to the next.
Phase shift = C
How far the function is shifted horizontally from its usual position.
(positive is to the left, negative is to the right).
Vertical shift = D
How far the function is shifted vertically from its usual position.
Parent function:
[tex]y=\sin(x)[/tex]
Therefore:
- Amplitude = 1
- Period = 2π
- Phase shift = none
- Vertical shift = none
Given function:
[tex]y=3\sin(2x)-1[/tex]
[tex]y=3\sin(2(x+0))-1[/tex]
Therefore:
- Amplitude = 3
- Period = π
- Phase shift = none
- Vertical shift = -1
**See attached images for how the parent function is transformed to the final function**
