Graph y=sin(x)+2

Problem

y=sin(x)+2

Solution

1. Identify the parent function, which is y=sin(x) The basic sine wave has a period of 2*π an amplitude of 1 and oscillates between −1 and 1

2. Determine the vertical shift by looking at the constant added to the function. In y=sin(x)+2 the +2 indicates a vertical shift upward by 2 units.

3. Find the new midline of the graph. The original midline y=0 (the x-axis) moves up to y=2

4. Calculate the range of the function. Since the amplitude is 1 and the midline is 2 the maximum value is 2 + 1 = 3a*n*d(t)*h*e*m*i*n*i*m*u*m*v*a*l*u*e*i*s() - 1 = 1$.

5. Plot key points over one period [0,2*π] The points (0,0),(π/2,1),(π,0),((3*π)/2,−1),(2*π,0) from the parent function shift to (0,2),(π/2,3),(π,2),((3*π)/2,1),(2*π,2)

6. Sketch the curve by connecting these points with a smooth, periodic wave.

Final Answer

To graph y=sin(x)+2 shift the graph of y=sin(x) upward by 2 units.

y=sin(x)+2

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