A graph is periodic if the y-values repeat at regular intervals. The amplitude is half the distance between the maximum and the minimum values. The period is the horizontal length of one cycle.
Is the Function Periodic? Yes. Period: 4 Amplitude: 2
Practice makes perfect
Looking at the given diagram, we can see that the y-values repeat at regular intervals. Therefore, the function is periodic. Let's first identify two cycles. Then we can find the period and the amplitude of the function. The period is the horizontal length of one cycle. Amplitude is half the distance between the maximum and the minimum values.
We can see that one cycle goes from - 3 to 1. A second cycle goes from 1 to 5. This is enough to find the period.
l1-(- 3)= 4 5-1= 4 ⇒ Period: 4
We can see that the maximum and minimum values are 2 and - 2, respectively. With this information we can find the amplitude.
Amplitude: 2-(- 2)/2= 2
