By James Stewart, Lothar Redlin, Saleem Watson, Phyllis Panman

This article bridges the distance among conventional and reform ways to algebra encouraging scholars to determine arithmetic in context. It offers fewer subject matters in higher intensity, prioritizing facts research as a origin for mathematical modeling, and emphasizing the verbal, numerical, graphical and symbolic representations of mathematical ideas in addition to connecting arithmetic to actual lifestyles occasions drawn from the scholars' majors.

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This leads us to the following definition of function. Definition of Function A function is a relation in which each input gives exactly one output. 2. The diagram in Figure 1(a) represents a function because for each input there is exactly one output. But the relation described by the diagram in Figure 1(b) is not a function—the input 2 corresponds to two different outputs, 20 and 30. 10 20 30 40 1 2 3 4 Inputs Outputs 1 2 3 4 10 20 30 40 50 Inputs Outputs (a) A function (b) Not a function f i g u r e 1 When is a relation a function?

9. 10. a b 55 0 - 10 1 52 1 -4 86 2 49 2 2 74 3 46 3 8 u v A B 5 0 110 0 1 12 1 98 2 19 2 3 26 3 4 4 4 4 5 5 5 5 6 6 6 6 11–14 ■ A set of data is given. (a) Find the first differences. (b) Is a linear model appropriate? If so, find a linear model for the data. (c) If there is a linear model, use it to complete the table. 11. First difference 12. x y 205 0 60 1 218 1 54 2 231 2 48 3 244 3 42 x y 0 4 4 5 5 6 6 13. First difference 14. 3 ■ 15–18 15. Equations: Describing Relationships in Data ■ Find a linear model for the data graphed in the scatter plot.

4 that a function is a relation in which each input gives exactly one output. In real-world applications of functions we need to know how the output is obtained from the input. In other words, we need to know the rule or process that acts on the input to produce the corresponding output. So we can define a function as the rule that relates the input to the output. Viewing a function in this way leads to a new and very useful notation for expressing functions, which we study in this section. 2 ■ Function Notation We previously used letters such as x, y, a, b, .