Question

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

Answer 1

Sin(x-pi) always range  from -1 to 1

which means :

y = 1 + 2 (-1 to 1)

y = 1 + (-2 to 2)

y = -1 to 3

hope this helps

Answer 2

Answer:

The range of the function 1+2sin(x-π) is:

          [-1,3]

Step-by-step explanation:

We have to find the range of 1+2sin(x-π)

sin(x-π)= -sin(π-x)    (since sin(-x)= - sinx )

now, sin(π-x)=sinx

since, the value of sinx lies between -1 and 1

i.e.     -1≤sinx≤1

⇒       -2≤2sinx≤2     (multiplying by 2)

⇒     -1≤1+2sinx≤3    (adding 1 on both sides)

Hence, the range of the function 1+2sin(x-π) is:

          [-1,3]