# Building Functions with Inverses

- Author:
- Tim Brzezinski

- Topic:
- Functions, Function Graph

## Interact with this app for a few minutes. LARGE POINTS are moveable. Then answer the questions that follow.

What do you notice? What do you wonder?

What does it mean for a relation to be a **function**? Describe. *Make sure to use the terms "input" and "output" in your description.*

In the app above, reposition the **3 LARGE POINTS** of the **function** so that the **graph of the inverse relation **also becomes a function.

Explain what you did to the **original function** to cause the **graph of the inverse relation** to be a function.

## Use this app to help you answer the questions that follow.

In the app above, reposition the **3 LARGE POINTS** of the **function** so that the **graph of the inverse relation is not **a function.

Explain what you did to the **original function** to cause the **graph of the inverse relation** to ** not be** a function.

Click on the **TEST INVERSE** checkbox. Drag the point that appears. How does this help illustrate the graph of the inverse relation is not a function? Explain. (*In your explanation, avoid using the phrase "vertical line test". Rather, describe using the terms "input" and "output".*)