Properties of Functions

This resource from Susan Wall contains five activities designed to enable students to explore the properties of functions in order to connect ideas together. Students learn how to solve equations, how to differentiate, how to find equations of tangents… but sometimes fail to see the picture as a whole. These resources encourage students to see how the techniques they have learned are applied to graphs of functions in order to help to understand the purpose of the mathematics. [b]Gradients[/b]: This activity links numerical values of dy/dx with the meaning at a particular point. Students have to match a statement about a graph with the value of dy/dx at a particular point. There is not a unique solution which leads to class discussion in which students give justification for their solution. [b]Properties of quadratic functions[/b]: This activity is designed to link together ideas for quadratic graphs; including solving equations and finding roots to differentials. For each of the statements beginning: ‘These functions … ‘, there are two functions in the list that will satisfy the statement. [b]Basic function notation[/b]: The aim of this activity is for students to familiarise themselves with the notation used when substituting a value into a function. Students find it relatively easy to work with f(x) and f’(x), but tend to get confused when asked to find the value of a function for a specific value of x e.g. f(9). This activity requires students to match each card with one of the four functions given. [b]Understanding function notation[/b]: This activity requires students to interpret statements about function notation. Students match a graph to its function and then place statements on the graphs at appropriate points, justifying their solutions. [b]Exploring functions[/b]: These activities require students to match the equation to the graph. The important part of the activity is for students to give as much evidence as they can to justify their answer.