See Examples 2, 3, 10, and 11 as you do Exercise.Health The following table shows the cons...

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

Health The following table shows the consumer price index (CPI) for medical care in selected years†:

(a) Let x = 0 correspond to 1950. Find the rule of a piecewise linear function that models these data—that is, a piecewise linear function f with f(0) = 15.1, f(25) = 47.5, and f(57) = 351.05. Round all coefficients in your final answer to one decimal place.

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(b) Graph the function f for 0 ≤ x ≤ 65.

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(c) Use the function to estimate the medical-care CPI in 2004.

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(d) Assuming that this model remains accurate after 2007, estimate the medical-care CPI for 2012.

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

†U.S. Bureau of Labor Statistics.