A cyclical function goes up and down in a repetitive manner. Does the number of graduating students follow this pattern?
B
b
Are you hungry and not hungry at the same time each day?
C
c
Coastal areas experience two low tides and two high tides every lunar day.
A
a
Not cyclical.
B
b
May or may not be cyclical.
C
c
Cyclical.
Practice makes perfect
a
A cyclical function is a continuous function that swings up and down in a repetitive manner as you move in the horizontal direction. The sine function is an example of such a function.
Now let's think about the number of students in each year's graduating class. Does this resemble a function that goes up and down in a repetitive manner? Well no! One year there might be 383 students graduating, followed by some other arbitrary number the following years. This does not match the characteristic of a cyclical function. Rather, we should use a step function.
b
When do we eat? Well, when we are hungry. The question becomes, does our hunger level go up and down in even intervals? Well usually we eat breakfast, lunch, and dinner, which would suggest that at those times we are hungry.
However, this is not necessarily true for everyone. So this may or may not be periodic.
c
Coastal areas experience two low tides and two high tides every lunar day, over 24 hours and 50 minutes. This is something that can be model with a cyclical function.
