Here we build some more formal definitions onto the understanding of properties of functions explored at Thinking about Functions.
We take a good look at the ideas of domain and range. The article Maths for dinner gives some context for domain and range within the formal language of functions, while Domain and range dominoes is a practical activity that requires students to think about and work out domains and ranges of a set of functions.
Domain and range are important considerations when it comes to composing functions. In the resource Compose! students are asked to work out which functions have been composed to make a given set of result functions, while in Composing gets me nowhere we investigate self-inverse functions.
Other ways of combining functions are explored in Function builder I, and in Translating or not? students are asked to sketch graphs of some reciprocal functions. Transformations of a parabola are the focus of Name that graph again and It’s a matter of perspective.
Resources addressing more introductory ideas around transformations and inverse functions will be coming shortly.
