Question

What is the range of the function y = 1 + 2sin(x − 3.14)?

Answer 1

Hello:
-1 ≤ sin(x- π ) ≤ 1
-2 ≤ 2 sin(x- π ) ≤2
1-2 ≤ 1+ 2 sin(x- π ) ≤ 1 +2
-1≤y≤3
the range is : [-1 : 3 ]

Answer 2

[-1,3].

Explanation:

The range of the function is the possible y-values that can be obtained. So, we know that the sin(x-3.14) always throws results between -1 and 1. That is

-1 ≤ sin(x-3.14) ≤ 1

and we have 1+2sin(x-3.14), then

1+2(-1) ≤ 1+2sin(x-3.14) ≤ 1+2(1)

1-2 ≤ 1+2sin(x-3.14) ≤ 1+2

-1 ≤ 1+2sin(x-3.14) ≤ 3.

Then, the range is [-1,3].