3 Extending functions: variables and graphs

The idea of a function as a relationship is sometimes called covariance; because it describes how two quantities vary together. If your learners go on to study advanced mathematics, they will need to be able to shift fluently between the process perspective on function (associated with rules, function machines and sequences) and the relationship (covariance) perspective.

In the middle years, the goal for most learners is to have a sound understanding of a function as a process and to develop some awareness of the representations related to functions that will prepare them to notice different kinds of covariance.

In this section you will meet some of the more advanced vocabulary and concepts associated with these representations.