Functions

Learning objectives

State the domain of a function and find its range, for example by completing the square or by sketching the graph over a restricted domain

Form composite functions such as fg(x) and gf(x), and explain why fg can be formed only when the range of g lies within the domain of f

Decide whether a function is one-one from its graph, and find the inverse of a one-one function by making x the subject, stating the domain of f⁻¹ as the range of f

Sketch y = f(x) and y = f⁻¹(x) on the same axes as reflections of each other in the line y = x

Describe and apply the transformations y = f(x) + a, y = f(x + a), y = af(x), y = f(ax), y = −f(x) and y = f(−x), and simple combinations of them, to algebraic and trigonometric graphs using the words translation, stretch and reflection