Inputs and outputs
In this step Paula and Michael demonstrate how a table of values can be generated using a function machine. Starting with a recap of a simple function machine they progress to consider a two-step function machine.
A connection with solving equations is made when Paula and Michael want to find what input is required to produce a given output.
In the final part of the video Paula and Michael explore how function machines can be linked with finding the position to term rule in a sequence by exploring what function machine produces a given table of inputs and outputs. More on this can be found in the course Understanding Numbers.
Task
This task will help you think about the connection between function machines and sequences. For each of the following tables, decide what function will produce the following inputs and outputs? Share your thoughts in the comments section below.
Function machine A
| INPUT | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| OUTPUT | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 |
Function machine B
| INPUT | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| OUTPUT | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Function machine C
| INPUT | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| OUTPUT | 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 |
Teaching resources
Worksheet questions
Now do question two from this week’s worksheet.
Maths Subject Knowledge: Graphs, Functions and Solving Equations Graphically
Maths Subject Knowledge: Graphs, Functions and Solving Equations Graphically
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