Question

A company monitored the number of major and minor earthquakes that occurred in a town. The graph below shows the number of monthly earthquakes in the town over 36 months.

The function describing this graph is a transformation of the parent sine function, y = sin x.

Which value best describes the period of the transformed function?
A.
6 months
B.
36 months
C.
12 months
D.
4 months

Answer 1

The graph shows the number of monthly earthquakes in the town over 36 months. To determine the period of the transformed function, we need to identify the length of one complete cycle on the graph. Looking at the graph, it appears that the cycle repeats every 12 months. Therefore, the best value that describes the period of the transformed function is C. 12 months.

Answer 2

C. 12 months

Explanation:

The period of a sinusoidal graph is defined as the horizontal distance between corresponding points on consecutive cycles, typically measured between consecutive peaks or troughs.

The peaks of the provided sinusoidal graph occur every April. Therefore, as the month of April occurs once a year, the period is 12 months.