The statement about reflecting periodic functions that is incorrect is:
C. A reflected periodic function will have the same period as the original function.
This statement is incorrect because when a periodic function is reflected over the x-axis, the period remains the same. However, when a periodic function is reflected over the y-axis, the period does not change. Reflecting a function over the y-axis affects the sign of the function, but not its period. Period refers to the length of one cycle of the function, and reflecting the function does not alter this fundamental characteristic.
For example, if you have a cosine function with a period of 2π, reflecting it over the x-axis will not change the period; it will still complete one cycle every 2π units along the x-axis. Reflecting it over the y-axis will change the sign of the function but will not impact the period.
Therefore, the correct understanding is that reflecting a periodic function over the x-axis does not alter its period, while reflecting it over the y-axis changes the sign of the function but not the period.
