The applet below graphically illustrates what it means for a function to be classified as an [color=#666666][b]ODD FUNCTION[/b][/color][b]. [br][/b] [br]No matter where you choose to place the WHITE POINTS, the [color=#666666][b]gray function will always remain an[br]ODD FUNCTION[/b][/color]. Feel free to place the [color=#1e84cc][b]BIG BLUE POINT[/b][/color] wherever you'd like as well. [br][br]After interacting with this applet for a few minutes, please answer the questions that follow.
Based solely upon your observations (and without looking it up on another tab in your web browser), describe what it means for a function to be classified as an [color=#666666][b]ODD FUNCTION[/b][/color].
What can you conclude about the graph of any odd function?
[i][b]Hint:[/b] [/i]Consider any symmetry that might be involved! (There are actually 2 [equivalent] ways to describe the special symmetry that exists in the graph of an odd function.)
Examine the function whose graph is shown in the applet below. [br]Feel free to adjust the value(s) of [i]a[/i] and/or [i]b[/i]. [br][br]I[color=#0000ff]s this the graph of an odd function? Algebraically show why, using your conclusion from (1) as the basis for your reasoning. [/color][color=#980000](Be sure to drag the [b]BIG BROWN POINT[/b] around!) [/color]
[b]Hint: [/b][br]For any given value(s) of [i]a[/i] and/or [i]b[/i], evaluate the function [i]f[/i] at an input value = -[i]x[/i]. If a function is an odd function, what is true about [math]f\left(-x\right)[/math]?