Plotting (linear) function machines

In this video, Paula and Michael explore the progression from using a function machine to generate outputs from given inputs, to generating coordinate pairs and plotting the coordinate pairs on a set of axes.

Time is spent explaining how the axes are numbered as this is a common mistake for some students. It is also pointed out the scale on the horizontal axes need not be the same as the scale on the vertical axis.

A further teaching point is the clear explanation that the horizontal axis is often referred to as the x axis and that the horizontal, or x axis, is used to represent the inputs used in the function machine. It is good practise to make clear the connections between:

• the horizontal axis, the x axis and the inputs to the function machine
• the vertical axis, the y axis and the outputs from the function machine

As the video progresses we see how the individual points can be joined using a straight line to represent many different inputs and outputs. We also see how the notation develops from inputs and outputs to describing the line using an algebraic equation expressed in terms of x and y.

In the next step Michael and Paula show how to plot a graph with more than one operation and we ask you to start considering how extra operations change the graph.