Functions, domain, range and key features of graphs

Learning objectives

Use function notation f(x), state the domain and range of a function, and explain why a domain may need restricting in a real context, for example to non-negative time

Explain the concept of an inverse function as the mapping that undoes f, and use the notation f⁻¹(x) to read a value backwards from a graph or table

Sketch the graph of a function from a formula, from a description or from a calculator display, labelling the axes with the quantities and units they represent

Identify the key features of a graph, namely the axis intercepts, maximum and minimum points, vertical and horizontal asymptotes, and symmetry

Find the point of intersection of two curves or of a curve and a line with technology, and use it to solve an equation of the form f(x) = g(x)

Transfer a graph accurately from the calculator screen to paper, choosing a sensible window and marking the scale and the key points