Compare and Contrast

Other chapters of this book discuss in detail several of the graphs you encounter in this chapter. The purpose of this chapter is to expand on material you have already covered by allowing you to experiment with it in a safe, painless way. Visual Formula provides a tool that allows you to go in this direction.

A key activity involves creating pairs of graphs. When you create pairs of graphs, you can explore changes in a relative manner. One graph can serve as a starting point or contrasting point for the other. As you go, keep in mind that instruction sets accompanying each exercise are intended to isolate your activities so that you can easily jump around the chapter and try experiments at random.

When you examine the graphs in this way, you gain a sense of the extent to which graphing the output of functions furnishes a stronger sense of how algebra relates to geometric visualization.

To work with the graphs in this chapter, use Visual Formula to set up the named equations and generate graphs of them. Many of the examples show that when you type an x in the Value field of your equation, Visual Formula automatically generates enough plotted values to draw a graph. In cases in which the default setting for the number of plotted points proves too small and results in a skewed graph, use the Points control in the bottom-left Chart panel of Visual Formula to set the graph so that more points for plotting are available.