HOW TO TELL IF THE GRAPH IS PERIODIC

Determine whether each function is periodic. If it is state the period.

Problem 1 :

Solution :

The graph shows a pattern of similar curves, but the y-values of one section of the graph does not match with the other section. So, the given graph is not periodic.

Problem 2 :

Solution :

The graph shows the pattern and the y-values in each section repeats at regular intervals in other sections of the graph. This function is periodic.

To find the period, let us find the coordinates of the point at the beginning of one cycle.

The horizontal length of one cycle is 8 units. So, the period is 8.

Problem 3 :

The graph shows the pattern and the y-values in each section repeats at regular intervals in other sections of the graph. This function is periodic.

Finding period :

The horizontal length of the periodic function is 4 units. So, period is 4.

Problem 4 :

Solution :

The graph shows the pattern and the y-values in each section repeats at regular intervals in other sections of the graph. This function is periodic.

Finding period :

The horizontal length of the periodic function is 4 units. So, period is 4.

Problem 5 :

Solution :

The given graph doesn't have pattern, so it is not a periodic.

Problem 6 :

Solution :

The graph above follows a pattern, but the y-values in one section does not match with y-values in other section. So, it is not periodic.

Problem 7 :

Solution :

The graph shows the pattern and the y-values in each section repeats at regular intervals in other sections of the graph. This function is periodic.

Finding period :

The horizontal length of the periodic function is 3 units. So, period is 3.

Problem 8 :

Solution :

The graph shows the pattern and the y-values in each section repeats at regular intervals in other sections of the graph. This function is periodic.

Finding period :

Distance between -2 to 3 :

|-2| = 2

|3| = 3

So, 2 + 3 = 5 units.

Then the period is 5.