See Examples 2, 3, 10, and 11 as you do Exercise.Natural Science The number of minutes of...

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

Natural Science The number of minutes of daylight in Washington, DC. can be modeled by the function

where x represents the number of days of the year, starting on January 1. Find the number of minutes of daylight on

(a) day 32.

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(b) day 90.

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(c) day 200.

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(d) day 270.

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(e) Graph g(x).

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(f) On what day is the number of minutes of daylight the greatest?

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