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Brainlag Learn / GCSE Maths

Functions and graph transformations

Function notation, composite and inverse functions, the shapes of standard graphs, translations and reflections of y = f(x), and the graphs of sin, cos and tan (Higher).

Lessons

  1. Function notationWhat f(x) means, working out f(3) and f(−2), writing f(a + 1) as an expression, and solving f(x) = k. 20 min, free, Higher tier
  2. Composite and inverse functionsOne function inside another, fg(x), and the function that undoes f, f⁻¹(x). 25 min, with the Graphing Calculator, free, Higher tier
  3. Recognising graphsLinear, quadratic, cubic, reciprocal and exponential graphs: what each looks like, tables of values, plotting and y = abˣ. 25 min, with the Graphing Calculator, Plus, Higher tier
  4. Translating graphsy = f(x) + a moves a graph up or down, y = f(x + a) moves it left or right. Points, turning points, equations and vectors. 25 min, with the Graph transformations simulation, Plus, Higher tier
  5. Reflections and trigonometric graphsy = −f(x) and y = f(−x), the graphs of sin x, cos x and tan x, exact values, and solving sin x = k and cos x = k. 25 min, with the Unit Circle, Plus, Higher tier

Practise and test

AQA, Pearson Edexcel and OCR are registered trade marks of their owners. Brainlag Learn is independent: it is not affiliated with or endorsed by any exam board, and every question on it is original.