Answer:

Step-by-step explanation:
The parent function of this graph is: y = sin(x)
The sine function is periodic, meaning it repeats forever.
Standard form of a sine function:

- A = amplitude (height from the mid-line to the peak)
- 2π/B = period (horizontal distance between consecutive peaks)
- C = phase shift (horizontal shift - positive is to the left)
- D = vertical shift
The parent function y = sin(x) has the following:
- Amplitude (A) = 1
- Period = 2π
- Phase shift (C) = 0
- Vertical shift (D) = 0
- Mid-line: y = 0
From inspection of the given graph:
- Amplitude (A) = 1

- Phase shift (C) = 0
- Vertical shift (D) = +3 (as mid-line is y = 3)

Substituting the values into the standard form:


Therefore, the equation of the given trigonometric graph is:

Answer:
Step-by-step explanation:
4y - 2(5 - y + 4) = 4y - 2(9 - y)
= 4y + 9*(-2) - y *(-2)
= 4y - 18 + 2y {Combine like terms 4y and 2y}
= 6y - 18
6y - 18 = 6*y - 6*3
= 6(y - 3)
6y- 18 = 2 *3y - 2*9
= 2(3y -9)
2(3y - 9) and 6(y- 3 ) are equivalent to 4y - 2(5- y +4)
Others are not equivalent
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