Domain and range with inverse functions

The  exercise appears under the Algebra II Math Mission. This exercise works with inverse functions in their diagram and graphical forms.

Types of Problems
There are two types of problems in this exercise:


 * 1) Complete the function diagram and determine true statements: This problem provides a set of ordered pairs that represent a function. The student is asked to place the arrows in the function diagram to represent the function, then determine if the function is invertible as it stands, and/or whether it can be restricted to become invertible.Darwif1.png
 * 2) Restrict the domain to make function invertible: This problem has the graph of a function that is not invertible. The student is asked to determine which of the restricted domains would allow the function to become invertible.Darwif2.png

Strategies
Knowledge of inverse functions, including horizontal line test, are encouraged to ensure success on this exercise.
 * 1) A function is invertible if it passes the horizontal line test, i.e., if all horizontal lines hit the graph at most once.
 * 2) The diagram of a function is invertible if each output has only one arrow heading into it.
 * 3) On the Complete the function diagram and determine true statements problem, if it is invertible the only answer to take is the one that says it is invertible. Otherwise, one option will explain why it is not invertible, and there is often (but not always) a restriction condition that can make the function invertible.
 * 4) A function is called one-to-one if it is invertible. This is also known as injective.
 * 5) Each option needs to be checked on Restrict the domain to make function invertible because there is often more than one correct answer.

Real-life Applications

 * 1) Inverse function "undo" mathematical operations and other functions. They allow the ability to solve equations involving various mathematical functions.
 * 2) Restricting function domains to make them invertible is important in many applications in business.