Different Kinds of Functions

In this activity, whenever you see 💬, stop and share your responses with your partner. If you have different responses, try to come to a consensus.

For 1 - 3, use the following instructions.

Use the simulation screen labeled “Numbers”. Note you can switch between simulation screens using the toolbar located below the function builder.

1. Build a function. Fill in the function builder and table. Access the input and output information by clicking the gray tabs above and below the function builder.

2. What is the output when the input is 10? Switch papers with a teammate and check that you found the correct output. 💬

3. Describe how to find the output for your function if given any input. Challenge yourself to describe in multiple ways.

For 4 - 8, use the following instructions.

Use the simulation screen labeled “Equations”. Note you can switch between simulation screens using the toolbar located below the function builder.

4. Build a custom function. Fill in the function builder and representations. Access the table and graph information by clicking the gray tabs above and below the function builder.

5. What is y when x is 100?

6. Manipulate your function in different ways. Describe the effects on the table, graph, and equation that each of your actions has.

Action	Effect on table	Effect on graph	Effect on equation
Click the up arrow on the addition operation

7. What does your graph look like? What other graphs can you make?

8. Briefly describe how different operations impact the graph of your function.

1. Addition
2. Subtraction
3. Multiplication
4. Division

Extension

Play with the game! Challenge yourself to figure out the mystery functions. They get tricky when you have two or three operations. Does your rule match the simulation's rule? Can there be more than one answer?