A previous post on Functions features resources aimed at older students; I thought it would be useful to look at resources for teaching younger students. 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.
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 on 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.
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.
The AQA Bridging the Gap resources includes a resource on introducing function notation; these resources are ideal for students who have completed the previous KS3 programmes of study but will be studying the new GCSE courses.
On Exam Solutions you will find an introduction to f(x) notation.
For further information on new content at GCSE see this page.