Game Development Reference
In-Depth Information
Compare and Contrast
Other chapters of this topic 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.
Linear Graphs
A linear function generates a graph characterized by a slope that does not change.
The line-slope-intercept equation provides a way to experiment with linear
equations. Here is the line-slope-intercept equation as you have seen it in pre-
vious chapters:
f ðxÞ¼mx þ b
or
y ¼ mx þ b
Drawing from Table 10.1, you can use this equation to generate a line with a
positive slope of 2 and a y-intercept at 3:
y ¼
2
x þ
3
