Graph y=sin(x)+1

Problem

y=sin(x)+1

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 +1 which moves the entire graph up by 1 unit.

3. Establish the new midline at y=1

4. Calculate the range of the function by adding 1 to the minimum and maximum values of the parent sine function, resulting in a range from 0 to 2

5. Plot the key points for one period [0,2*π] starting at the midline: (0,1) (π/2,2) (π,1) ((3*π)/2,0) and (2*π,1)

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

Final Answer

y=sin(x)+1

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