Find the Range y=1+2sin(x-pi)

Problem

y=1+2*sin(x−π)

Solution

1. Identify the parent function and its range. The basic sine function sin(x−π) oscillates between −1 and 1

Range of *sin(x−π)=[−1,1]

2. Apply the amplitude. Multiply the range of the sine function by the coefficient 2

−1≤sin(x−π)≤1

−2≤2*sin(x−π)≤2

3. Apply the vertical shift. Add 1 to all parts of the inequality to account for the constant term in the function.

−2+1≤1+2*sin(x−π)≤2+1

4. Simplify the inequality to find the minimum and maximum values of y

−1≤y≤3

Final Answer

Range: *[−1,3]

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