Problem requiring decisions

## Taking it further

Now we have described the graphs in words, we want to see if we can describe the graphs using mathematical notation. How can we write the equations of these graphs?

You may wish to use the equation cards to help you. Try to match the graphs to their equations. You may find that you need to draw some extra graphs, and write some more equations to complete the set.

### Graph 1

Each section of the function is made up of equations in the form $y=a$.

The open and closed circles should have reminded us of representing inequalities on a number line.

### Graph 2

The middle section of the graph might have reminded us of a modulus function, as it could be part of the graph of $y=|2x|$.

But the modulus (or absolute value) function is a piecewise function itself, and can be written,

$f(x) = \begin{cases}-2x & \text{if } x<0 \\ 2x & \text{if } x≥0 \end{cases}.$

### Graph 3

Points $(3,0)$ and $(8,0)$ could be part of two different sections. Have we seen this before?

### Graph 4

Piecewise functions do not have to be linear, so having a quadratic as one of the sections is not a problem. Note that the final section continues as $x$ increases and doesn’t have an end point.

### Extra equations

There are two cards left that we haven’t looked at yet. Can you draw the graphs for them? Are they both functions?