The applet below dynamically depicts what it means for a function to be classified as a [color=#9900ff][b]periodic[/b][/color][b] function. [br][br][/b]Interact with the applet below for a few minutes. [br]As you do, be sure to move the 5 points anywhere you'd like. [br]Answer the questions that follow.
What does the term "periodic" mean? What events in life would you classify as predictably "periodic"? Why would you classify these events this way?
The [b][color=#9900ff]length of the purple segment[/color][/b] is said to be the [b][color=#9900ff]period[/color][/b] of the function [i]f[/i]. Suppose the [b][color=#9900ff]period[/color] [/b]of the function above = [b][color=#9900ff]5 units[/color][/b]. Also, suppose [i]f[/i](2) = 8. Given this information, [b]what other input values for function [i]f[/i] would also result in an output of 8?[/b]
Suppose a function [i]f[/i] has [b][color=#9900ff]period [i]c[/i][/color][/b]. How would you describe what it means for a function [i]f[/i] to be periodic in terms of [i]x[/i] and [b][color=#9900ff]c[/color][/b]?