# Function Notation Worksheet • Section 1 of the function notation worksheet contains 27 skills-based function notation questions, in 3 groups to support differentiation
• Section 2 contains 4 applied questions with a mix of worded problems and deeper problem solving questions
• Section 3 contains 4 foundation and higher level GCSE exam practice questions for function notation practice, including evaluating the function f for various values
• Answers and a mark scheme for all questions are provided
• Questions follow variation theory with plenty of opportunities for students to work independently at their own level
• All questions created by fully qualified expert secondary maths teachers
• Suitable for GCSE maths revision for AQA, OCR and Edexcel exam boards

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### Function notation at a glance

A function is a relationship between two variables.  There is a special notation for writing functions, such as f(x) which is read as the ‘function of x’. Each function within a question may be represented by a different letter such as f, g or h.

Evaluating functions requires us to substitute a value for x in the algebraic expression. Functions may be linear expressions or more complex polynomials or even algebraic fractions.

Functions can be used to produce pairs of coordinates (ordered pairs) and thus used to produce graphs of functions. Linear functions produce straight line graphs and quadratic functions produce curves.

Inverse functions have a special notation which looks like f-1(x) and composite functions have a notation which looks like fg(x) which is read as ‘f of g of x’.

We can also use our knowledge of function notation to produce situations where equations can be formed and solved.

Looking forward, students can progress with more functions worksheets to additional algebra worksheets, for example a simplifying expressions worksheet or simultaneous equations worksheet. For more teaching and learning support on Algebra our GCSE maths lessons provide step by step support for all GCSE maths concepts.

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