Question

Determine the period of the following graph

Answer 1

Explanation:

the period of a function or graph is simply the x-distance from one "top of the hill" to the next "top of the hill", or from one "bottom of the valley" to the next "bottom of the valley".

if the function has that same distance across the whole x-axis (or whatever part is valid), we are calling this a periodic function.

in our case here :

from -9pi to 3pi = 12pi

from 3pi to 15pi = 12pi

from 15pi to 27pi = 12pi

...

so, yes, it is periodic, and the period is 12pi.

Answer 2

period = 12π

Explanation:

the period illustrates how shifting the graph by one period to the left or right results in the same function.

starting from (0, 3 )

one complete cycle to the right from here is (12π, 3 )

then period = 12π - 0 = 12π