Linear Functions

Functions are one of the building blocks of algebra. Variables represent quantities, but by themselves they don’t tell you much. Functions tell you how those variables relate to each other. The Linear Functions Gizmo allows students to build their own relations and test them to see if they are functions, and if they are, to also see if they are linear.

The Gizmo allows students to create their relations either by dragging an arrow in an input-output mapping diagram, or by placing a point on a graph. Each arrow also creates a point on the graph, and likewise, each point creates a new arrow. Placing these two side-by-side, and having them work in conjunction like this, drives home the connection between these ways of representing a relation.

When is a relation a function? When is a function linear? Can a relation be linear but not a function? This Gizmo can facilitate a lot of thought-provoking explorations like these, for you and your students.