What is the range of the function y = 1 + 2sin(x - π)?

Solution:

Given, the function is y = 1 + 2sin(x - π)

We have to find the range of the function.

By using trigonometric identity,

sin(-x) = -sin(x)

So, sin(x - π) = -sin(π - x)

Again, using trigonometric identity,

sin(π - a) = sin a

So, -sin(π - x) = -sin(x)

The value of sin(x) lies between -1 and 1.

i.e. -1 ≤ sin(x) ≤ 1

Multiplying by 2 on both sides,

-2 ≤ 2sin(x) ≤ 2

Adding 1 on both sides,

1 - 2 ≤ 1+ 2sin(x) ≤ 2 + 1

-1 ≤ 1 + 2sin(x) ≤ 3

Range = [-1, 3]

Therefore, the range of the function is [-1, 3].

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What is the range of the function y = 1 + 2sin(x - π)?

Summary:

The range of the function y = 1 + 2sin(x - π) is [-1, 3].