Pearson Edexcel · A-Level · Mathematics
Course version: 9MA0 · Version from Mar 2026
Mathematical argument, language and proof: Understand and use the…
Full specification wording
Overarching theme 1: Mathematical argument, language and proof: Understand and use the definition of a function; domain and range of functions.
A function is a mathematical mapping that assigns exactly one output value to each valid input value.
Checked against the Pearson Edexcel 9MA0 specification (opens in a new tab) on .
- Point 4 of 5
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A function is a mathematical mapping that assigns exactly one output value to each valid input value. You must understand this definition to distinguish functions from general relations; for instance, a circle equation is not a function because one x-value can yield two y-values. The domain is the complete set of possible input values (x-values) for which the function is defined, while the range is the corresponding set of output values (y-values or f(x)). For example, the function f(x) = x² with a domain of all real numbers (x ∈ ℝ) has a range of f(x) ≥ 0. You must be able to determine the domain and range for various functions, including linear, quadratic, trigonometric, exponential, and rational functions, often by sketching their graphs.
What earns the marks
- Identify whether a given mathematical relation constitutes a function by checking if each input maps to exactly one output.
- Determine the maximal domain of a function by identifying restricted values, such as denominators that equal zero or negative values under a square root.
- Calculate or deduce the range of a function based on its given domain, often utilising the vertex of a quadratic or the asymptotes of a rational function.
- Use appropriate set notation or inequalities to state the domain and range clearly.
Common mistakes and how to put them right
Confusing domain and range.
Put it right: The domain refers to the input values (usually x) and the range refers to the output values (usually f(x) or y).
Assuming the range of a quadratic function is all real numbers.
Put it right: The range is restricted by the maximum or minimum value at the vertex, so always find the turning point.
Stating the range using the variable x instead of f(x) or y.
Put it right: Use the correct variable to denote the output values of the function.
Exam tips
- Sketching the graph of the function is the most reliable method for finding its range, as it visually highlights minimums, maximums, and asymptotes.
- When finding the domain of a rational function, set the denominator equal to zero to find the values that must be excluded.
- Pay close attention to restricted domains given in the question, as these will directly impact the corresponding range you need to calculate.
Try the lesson
The start of the Overarching theme 1: Mathematical argument, language and proof: Understand and use the definition of a function; domain and range of functions. lesson, made from checked teaching notes for this specification point.
Have a go first
The function h is defined by h(x) = 1 / √(2x - 5). What is the maximal domain of h?
Listen
A function is a mathematical mapping that assigns exactly one output value to each valid input value. You must understand this definition to distinguish functions from general relations; for instance, a circle equation is not a function because one x-value can yield two y-values. The domain is the complete set of possible input values (x-values) for which the function is defined, while the range is the corresponding set of output values (y-values or f(x)). For example, the function f(x) = x² with a domain of all real numbers (x ∈ ℝ) has a range of f(x) ≥ 0. You must be able to determine the domain and range for various functions, including linear, quadratic, trigonometric, exponential, and rational functions, often by sketching their graphs. A strong answer earns marks for these points. Identify whether a given mathematical relation constitutes a function by checking if each input maps to exactly one output. Determine the maximal domain of a function by identifying restricted values, such as denominators that equal zero or negative values under a square root. Calculate or deduce the range of a function based on its given domain, often utilising the vertex of a quadratic or the asymptotes of a rational function. Use appropriate set notation or inequalities to state the domain and range clearly. Exam tip: Sketching the graph of the function is the most reliable method for finding its range, as it visually highlights minimums, maximums, and asymptotes.
Key words
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Function
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Domain
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Range
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See every definition
- Function
- A mathematical mapping that assigns exactly one output value to each valid input value.
- Domain
- The complete set of possible input values (x-values) for which the function is defined.
- Range
- The corresponding set of output values (y-values or f(x)) of a function.
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