Graph y=sin(x)-2

Problem

y=sin(x)−2

Solution

1. Identify the parent function and its properties. The base function is y=sin(x) which has an amplitude of 1 a period of 2*π and oscillates around the midline y=0

2. Determine the vertical shift by looking at the constant term. The value −2 indicates a vertical translation downward by 2 units.

3. Establish the new midline for the graph. The horizontal center of the wave moves from y=0 to y=−2

4. Plot the key points over one period [0,2*π] by subtracting 2 from the standard ycoordinates of the sine function.

• At x=0 y=sin(0)−2=−2

• At x=π/2 y=sin(π/2)−2=1−2=−1

• At x=π y=sin(π)−2=−2

• At x=(3*π)/2 y=sin((3*π)/2)−2=−1−2=−3

• At x=2*π y=sin(2*π)−2=−2

5. Draw the smooth curve through these points, ensuring the graph stays between the maximum value of −1 and the minimum value of −3

Final Answer

y=sin(x)−2

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