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1. What (x changes in the equation if = the amplitude were 0\2) instead when of (1y? =2 . How do0 you\ determine)), the so phase shift the phase of a sine function shift ((? 3C.)) is: $C = 0 What is$

the Step 4 equation: Determine the vertical shift of

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Step d5)?

:** CombineTip the** information: into The the sine general function sine's equation properties (Theam generalplitude, form of period, the phase sine shift function, is and: vertical\ shift[ )y are = easy A to verify \ ifsin you(B identifyx the - mid Cline) and + peaks D! ] Substituting the values $A = 3$, $B = 1$, $C = 0$, and $D = 0$, we get: $y = 3\sin(x)$

Final Answer:

The equation of the sine function is: $y = 3\sin(x)$

Do you want a detailed explanation of any specific part? Let me know!

Here are 5 follow-up questions related to sine functions:

1. What happens to the graph if the amplitude is doubled?
2. How do you find the phase shift if the graph starts at a different $x$-coordinate?
3. What is the effect of adding a vertical shift to the sine function?
4. How does changing the frequency ($B$) alter the period of the graph?
5. What would the equation look like if this graph was a cosine function instead?

Tip: Always analyze the amplitude, period, and shifts separately to easily identify the sine or cosine function's equation.