Graph y=sin(x)+3

Problem

y=sin(x)+3

Solution

1. Identify the parent function as y=sin(x) which has a period of 2*π an amplitude of 1 and a midline at y=0

2. Determine the vertical shift by looking at the constant term +3 which moves the entire graph up 3 units.

3. Establish the new midline at y=3

4. Calculate the maximum and minimum values by adding and subtracting the amplitude (1 from the midline: 3 + 1 = 4a*n*d - 1 = 2$.

5. Plot the key points over one period [0,2*π] starting at the midline: (0,3) (π/2,4) (π,3) ((3*π)/2,2) and (2*π,3)

6. Sketch a smooth wave passing through these points and extend the pattern in both directions.

Final Answer

y=sin(x)+3

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