See Examples 2, 3, 10, and 11 as you do Exercise.Finance The Alabama state income tax for...

See Examples 2, 3, 10, and 11 as you do Exercise.

Finance The Alabama state income tax for a single person in 2009 was determined by the rule

where x is the person’s taxable income in dollars. Graph the function T(x) for taxable incomes between 0 and $5000.

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 1.

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