Functions: notation, domain, range, composite and inverse

Learning objectives

Write the equation of a straight line in gradient–intercept, point–gradient and general form, find gradients and intercepts, and use the gradient conditions for parallel (m₁ = m₂) and perpendicular (m₁m₂ = −1) lines

Understand a function as a rule that assigns exactly one output to each input, use function notation, and state the domain and range of a function from its rule, its graph or its context

Interpret a function as a mathematical model of a real situation, use it to evaluate and predict, and comment on whether the domain is appropriate

Form composite functions such as (f ∘ g)(x) = f(g(x)), state their domains, and recognise the identity function

Find the inverse function f⁻¹(x) algebraically, relate its graph to a reflection in the line y = x, and use the fact that the domain of f⁻¹ is the range of f

(HL) Classify functions as odd, even or neither, restrict a domain so that an inverse function exists, and identify self-inverse functions