Looking at some favourite resource websites, some recommended resources for teaching functions …
For an excellent introduction the PhET Simulation, Function Builder provides a very visually appealing resource. Using the pattern option even very young students could explore important concepts. This is very intuitive to use, the slides in the following slideshow demonstrate examples of its use. Note that teachers can register with PhET and gain access to supporting documentation.
Desmos can be used very simply to illustrate function notation and note the use of Desmos as a calculator to evaluate the value of a function for a given input.
From White Rose Maths, we have Year 7 work on algebraic thinking, including function machines, and in Year 11, Functions.
As always CIMT is worth a search; we find:
In the interactive materials for year 7: Unit 16 Section 2: Function Machines and there is also a section in the associated text (16.2). All CIMT resources are free to access, a small number of documents such as text answers are password protected, you can obtain the CIMT password. These exercises could be used as an introduction and students also shown function notation. They could write the functions described by the function machines using f(x) notation.
The AQA Bridging the Gap resources includes a resource on introducing function notation; These resources were originally designed to support teaching and learning for students who studied the 2007 Key Stage 3 Programme of Study and were preparing for the then new Mathematics GCSE. The resources are still very useful.
On Transum, try this online exercise on function notation, inverse functions and composite functions.
There are also many more activities on functions on Transum.
For a challenging problem on Function Notation, try this from Open Middle.
From Andy Lutwyche, a resource I have always liked is one of his excellent Building Blocks series on Function Notation. We can also search his site on functions. (I am so pleased to see Andy’s resources on his own site, andylutwyche.com.)
Or we could help Clumsy Clive with his homework on Function Notation.
From CorbettMaths try the Practice Questions.
On DrFrostMaths, try the Functions Key Skills.
From Don Steward, try these lovely questions on Compound Functions.
From MathsHKO see Function Machines, and also Functions.
We could simplify expressions on Graspable Math
On Starting Points Maths, a search on Functions returns several tasks, including work on Graphs and Transformations.
On Maths Genie, under Grade 7, we have Inverse and Composite Functions. You will find some revision examples and also exam questions with solutions.
For a compilation of GCSE questions, William Neill’s GCSE Maths Questions site is so useful. Under Algebra, we see A7 Function Machines and A65-68 (H) Functions.
On MathsBot we could use GCSE Exam Style Questions for higher questions on Composite functions.
Or use a GCSE Revision Grid.
On TES, this Crossnumber from cbarthur is an ideal resource for becoming familiar with function notation. Also on TES from Owen134866 we have a set PowerPoint resources including an introduction to f(x) notation for GCSE students.
From OCR, Check in tests can be very useful, consider the language of functions for example, the first questions could be used for students as young as Year 7 (age 11-12).
See also these very clear notes with exercises from Plymouth University including Functions..