[color=#000000]Recall that, for any relation, the graph of this relation's inverse can be formed by reflecting the graph of this relation about the line y = x. [br][br]Recall that all functions are relations, but not all relations are functions. [br]Again, what causes a relation to be a function? Explain. [br][br]In the applet below, you can input any function [i]f[/i] and restrict its natural domain, if you choose, to input (x) values between -10 and 10. You also have the option to graph the function over its natural domain. [br][br]Interact with this applet for a few minutes, then complete the activity questions that follow. [/color]

[color=#000000][b]Directions: [/b][br][br]1) Choose the [b]"Default to Natural Domain of f"[/b] option. [br]2) Enter in the [/color][color=#980000][b]original function[/b][/color][math]f\left(x\right)=0.2x^2[/math][color=#000000]. [br]3) Choose [/color][color=#38761d][b]"Show Inverse Relation"[/b]. [/color][br][color=#000000]4) Is the [/color][color=#38761d][b]graph of this inverse relation[/b][/color][color=#000000] the graph of a function? Explain why or why not. [br]5) If your answer to (4) above was "no", uncheck the [b]"Default to Natural Domain of f"[/b] checkbox. [br]6) Now, can you come up with a set of Xmin and Xmax values so that the function shown has an inverse [br] that is a function? Explain. [br][br]At any point in this investigation, do the following:[br][br]Use the [b]Point On Object[/b] tool to plot a point on the original function.[br]Then, use the [b]Reflect About Line[/b] tool to reflect this point about the line y = x. [br]What do you notice about the coordinates of this point's reflection? Where does this point lie? [br][br]Repeat steps (1) - (6) again, this time for different functions [i]f[/i] provided to you by your instructor. [/color]