To find the range of the function y = 12sin(x) + p, we need to understand how the sine function behaves and how it is affected by the transformations applied to it.
The sine function, sin(x), oscillates between -1 and 1. Therefore, when we multiply it by 12, the range of 12sin(x) becomes:
-12 <= 12sin(x) <= 12.
Now, if we add p to the function, this is a vertical shift of the entire graph. In other words, the minimum and maximum values of the function will both increase by p.
This leads us to determine the new range as follows:
- Minimum value: -12 + p
- Maximum value: 12 + p
Hence, the range of the function y = 12sin(x) + p can be expressed as:
Range: (-12 + p, 12 + p).
In conclusion, the range of the function depends on the value of p, which shifts the sine curve up or down the y-axis. This can be summarized as:
Range = [p - 12, p + 12]where p is any real number.