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A function maps each input to one output; its domain is the allowed inputs and its range the possible outputs. This topic covers function notation, identifying domain and range and one-to-one and many-to-one functions. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
The domain is the set of inputs allowed and the range is the set of outputs produced. Rule out values that would divide by zero or take the root of a negative. Sketching the graph makes the range readable directly.
Before you start
It assumes you can handle function notation and graph sketching. Getting it right here pays off in composite and inverse functions.
What you learn
The domain of a function is the set of inputs it is allowed to take; the range is the set of outputs it produces. In P3 you must find both for the full function library — quadratics, roots, reciprocal functions (including those built from e^x and logarithms) and trigonometric functions — and connect the range of a function to the domain of its inverse. Some expressions restrict which inputs are allowed. Over a restricted domain, compare the turning point with the endpoint values. The course works through domain and range, finding the domain, range of quadratics & roots, range of reciprocal functions, reciprocals of exponentials & logs and range of trigonometric functions. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Functions - Domain and Range is a Algebra topic in the A-level syllabus, covered here at the AS year. You work through 6 concepts and 6 worked examples, testing yourself at 6 points. It sits alongside Improper Algebraic Fractions, Indices and Surds, Inequalities, Modulus Function and Partial Fractions in the same strand. For unlimited practice, the Algebra revision engine builds new questions on demand and records your accuracy.
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