Inverse Relations: Graphs
- Tim Brzezinski
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. Recall that all functions are relations, but not all relations are functions. Again, what causes a relation to be a function? Explain. In the applet below, you can input any function f 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. Interact with this applet for a few minutes, then complete the activity questions that follow.
Directions: 1) Choose the "Default to Natural Domain of f" option. 2) Enter in the original function. 3) Choose "Show Inverse Relation". 4) Is the graph of this inverse relation the graph of a function? Explain why or why not. 5) If your answer to (4) above was "no", uncheck the "Default to Natural Domain of f" checkbox. 6) Now, can you come up with a set of Xmin and Xmax values so that the function shown has an inverse that is a function? Explain. At any point in this investigation, do the following: Use the Point On Object tool to plot a point on the original function. Then, use the Reflect About Line tool to reflect this point about the line y = x. What do you notice about the coordinates of this point's reflection? Where does this point lie? Repeat steps (1) - (6) again, this time for different functions f provided to you by your instructor.