1. Functions and mappings
A3.2 Core Starter
Here are some function machines.
Link them together to form a machine chain that gives the largest possible output when the input is 1.
Now rearrange the function machines so that, when the largest output that you have just found is the input of the new chain, the output is 1.
× 2
− 5
÷ 2
+ 5
Preamble
Pupils are given the opportunity to practise using function machine chains and in the last part to use their knowledge of inverse function machines. The task is suitable for individuals or small groups, with the collection of results/conclusions at the end.
Possible content
Function machines, simple arithmetic and inverse function machines.
Resources
None.
Solution/Notes
The largest possible output is 6:
Use the inverse operations to map this maximum value back to 1: or
÷ 2
+ 5 1
× 2 6
− 5 or
+ 5
÷ 2 6
− 5 1
× 2