Graph y=-2sin(x)

Problem

y=−2*sin(x)

Solution

1. Identify the parent function and its key characteristics. The parent function is y=sin(x) which has a period of 2*π an amplitude of 1 and passes through (0,0) (π/2,1) (π,0) ((3*π)/2,−1) and (2*π,0)

2. Determine the amplitude of the given function. The coefficient of the sine function is −2 The amplitude is the absolute value |−2|=2 meaning the graph will oscillate between y=2 and y=−2

3. Identify the reflection across the x-axis. Because the coefficient is negative (−2, the graph of sin(x) is reflected vertically. Instead of starting by moving upward to a maximum, the graph moves downward to a minimum.

4. Determine the period of the function. The coefficient of x is 1 so the period remains 2*π

5. Plot the key points for one full cycle. Using the transformations, the points are:

   (0,0)

   (π/2,−2)

   (π,0)

   ((3*π)/2,2)

   (2*π,0)

6. Sketch the curve by connecting these points with a smooth wave pattern and extending it in both directions.

Final Answer

y=−2*sin(x)

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