Graph the function. (See Examples 1–4.)Example 1The graph of the function g(x) = .5x − 3 i...

Graph the function. (See Examples 1–4.)

Example 1

The graph of the function g(x) = .5x − 3 is the graph of the equation y = .5x − 3. So the graph is a graph is a straight line with slope .5 and y-intercept −3, as shown in Figure 1.

Example 2

Graph the following function:

Solution

Consider the two parts of the rule of f. The graphs of y = x +1 and y = −2x + 7 are straight lines. The graph of f consists of

Each of these line segments can be graphed by plotting two points in the appropriate interval, as shown in Figure 2.

Note that the left and right parts of the graph each extend to the vertical line through x = 2, where the two halves of the graph meet at the point (2, 3).

FIGURE 1

FIGURE 2