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LearnCambridge97092026–2027Paper 1 · Pure Mathematics 1Functions

Paper 1 · Module

Functions

5 subtopics≈ 200 min in total

Start the module: Functions, domain and range Open graphing calculator

Functions, domain and range
What makes a rule a function, function notation, the largest possible domain, and how to find the range of linear and quadratic functions on any domain.
≈ 40 min
Composite functions
Applying one function after another: what $fg(x)$ means, finding and solving with composite expressions, and when a composite function exists.
≈ 35 min
One-one and inverse functions
Which functions can be undone, how to find $f^{-1}(x)$ , why the domain of the inverse is the range of the function, and how to invert a quadratic on a restricted domain.
≈ 45 min
Graphs of a function and its inverse
Why the graph of $f^{-1}$ is the reflection of $f$ in the line $y=x$ , how points, intercepts and asymptotes swap over, and where a function meets its own inverse.
≈ 30 min
Transformations of graphs
Translating, stretching and reflecting $y=f(x)$ : what each of $f(x)+a$ , $f(x+a)$ , $af(x)$ and $f(ax)$ does, how to describe it in exam language, and how to combine transformations in the right order.
≈ 50 min