Glossary
Amplitude
Half the distance between the maximum and minimum output values of a periodic function, representing the maximum displacement from the equilibrium position.
Example:
If a swing moves 3 feet forward and 3 feet backward from its resting position, its amplitude is 3 feet.
Concavity
Describes the direction in which the graph of a function opens, either upward (concave up) or downward (concave down). In periodic functions, concavity patterns repeat.
Example:
The path of a thrown ball initially shows concavity downward as it rises and then falls, and if it were to bounce repeatedly, this pattern of concavity would repeat.
Cycle
One complete repetition of the pattern in a periodic function.
Example:
One full rotation of the minute hand on a clock, taking 60 minutes, represents a single cycle.
Intervals of Increase and Decrease
Specific ranges of input values where a function's output values are consistently rising or falling, respectively. In periodic functions, these intervals repeat.
Example:
In a typical year, the average daily temperature in a city shows intervals of increase during spring and summer, and intervals of decrease during autumn and winter, repeating annually.
Period
The length of one complete cycle, representing the smallest interval over which a periodic function repeats its behavior.
Example:
If a person's heart beats 72 times per minute, the period of one heartbeat is approximately 0.83 seconds.
Periodic Relationships
A relationship where output values repeat themselves as input values increase, occurring over equal intervals.
Example:
The daily high tide and low tide levels in a harbor follow a periodic relationship, repeating approximately every 12 hours and 25 minutes.
Rates of Change
How quickly the output value of a function changes with respect to its input value. In periodic functions, the pattern of rates of change repeats.
Example:
The rates of change for the amount of daylight throughout the year will show a repeating pattern, increasing most rapidly around the equinoxes and slowing near the solstices.
Repeating Patterns
A sequence of output values that occurs identically multiple times within a function's domain.
Example:
The phases of the moon, from new moon to full moon and back, form a repeating pattern over approximately 29.5 days.