The function y = 2sin(x) is a transformation of the basic sine function, which has a known range. To understand the range of this function, let’s first recall a couple of key points about the sine function:
- The basic sine function, sin(x), has a range of [-1, 1].
- This means that the function sin(x) will output values between -1 and 1, inclusive.
Now, when we multiply the sine function by 2, as in y = 2sin(x), we are effectively stretching the range of the function vertically by a factor of 2. To find the new range, we can simply multiply the original range of the sine function by 2:
- Minimum value: -1 × 2 = -2
- Maximum value: 1 × 2 = 2
Therefore, the range of the function y = 2sin(x) is:
- [-2, 2]
In summary, the function y = 2sin(x) oscillates between -2 and 2, reaching these extreme values when sin(x) is at its maximum and minimum values of 1 and -1, respectively. This means that for any value of x, the corresponding value of y will always fall within the range of -2 to 2.