Question

A homeowners' association monitored the number of households in a neighborhood using their sprinkler systems during certain hours. The function describing this graph is a transformation of the parent cosine function, y = cos x. Which value best describes the period of the transformed function?

A) 24 hours
B) 12 hours
C) 18 hours
D) 16 hours

Answer 1

The period of the transformed cosine function that best describes the usage of sprinkler systems is 24 hours because it is suggested that the function repeats every 12 hours or operates at half-power for a full day.

Step-by-step explanation:

The student is asking about a transformation of the parent cosine function and its period, given that this function describes the usage of sprinkler systems in a neighborhood. The period of a function is the duration after which the function starts to repeat its values. The period of the standard cosine function, y = cos(x), is 2π, which represents a complete oscillation in the unit circle and corresponds to 360 degrees or, in terms of time, could represent a full day or 24 hours. When the cosine function is transformed by a horizontal stretching or compressing, the period changes. If the function repeats every 12 hours or alternatively is at half-power for 24 hours as suggested by the hint, the best description for the period of the transformed function would be 24 hours, because a full cycle of on-off-on would complete in that time frame.