### Thinking about Functions

Package of problems

# Mapping a function Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

## Warm-up

In this resource, we will explore linear functions and how they can be represented. This is interesting in its own right, and also gives us a tool to think about an important idea in calculus. We will take this further in Mapping a derivative.

Here are mapping diagrams representing functions of the form $f(x)=ax+b$ for $x\in\mathbb{R}$.

(In these diagrams, the left-hand numberline is the input and the right-hand one is the output, for example in Diagram 1, $f(1)=3$.)

 Diagram 1 Diagram 2 Diagram 3 Diagram 4 Diagram 5 Diagram 6
• What do you notice about these diagrams and the functions they represent? (You might find it helpful to work out some or all of the functions first.)

• What features do the diagrams and functions have in common? What are the differences between them?