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# Regions and their Signed Areas

## 8.2.1 Highlighting Regions in GC

As explained in Chapter 3, GC is built to create graphs. It is designed to interpret anything you type as either a definition of a mathematical term (e.g., a function) or a command to display a graph. Whenever you type a well-formed statement, other than a definition, GC will attempt to display a graph of the ordered pairs or ordered triplets that make that statement true.

We describe regions in the plane by stating conditions that points in the plane must satisfy to be considered in that region. For example, the mathematical statement $\left\{(x,y)\mid x^2+y^2\le 1\right\}$, read as "The set of all points with coordinates x and y such that ...", describes the set of points in Figure 8.2.0. GC highlighted all the points in the Cartesian plane that have coordinates x and y such that $x^2+y^2\le 1$.

Figure 8.2.0. Typing $x^2+y^2\le 1$ into GC told it to highlight all the points in the plane whose coordinates satisfy that condition.

Notice that in Figure 8.2.0 we typed only the condition part of the mathematical statement $\left\{(x,y)\mid x^2+y^2 \le 1\right\}$. This is because GC always interprets any non-definitional statement involving x or y as a command to "highlight all the points (x,y) such that ...".