See Examples 2, 3, 10, and 11 as you do Exercise.Finance The maximum allowable yearly cont...

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

Finance The maximum allowable yearly contribution to an individual retirement account (IRA) was $2000 from 1981 to 2001 and has increased steadily since then. When the maximum is adjusted for inflation, however, the picture is a little different. The approximate maximum IRA contribution in 1981 dollars in year x is given by the function

where x = 0 corresponds to 1980.

(a) Graph this function.

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(b) What does the graph say about inflation from 1981 to 2001?

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