Section 2.6 Introduction to Functions 195 x 5, Thus, when the corresponding function value is 10.We say: • f of 5 is 10. • f at 5 is 10. • f evaluated at 5 is 10. The names of functions are often given by either lowercase or uppercase letters, such as f, g, h, p, K, and M. The input variable may also be a letter other than x. For example, the function y P(t) might represent population as a function of time. Evaluating a Function Given the function defined by find the function values. a. g102 b. g122 c. g142 d. g122 Solution: a. b. 1 2 1 2 122 g102 1 0 1 1 1 1 0 We say that “g of 0 is 1 .” We say that “g of 2 is 0.” This 10,is equivalent 12. to the ordered This 12,is equivalent 02. to the ordered pair pair g122 1 2 102 1 g1x2 1 2 g1x2 x 1 x 1 g1x2 12 x 1, Example 3 1 2 g1x2 x 1 c. x 1 d. 1 2 g1x2 1 2 122 g142 1 g122 1 2 142 1 2 1 1 1 We say that “g of 4 is 1.” We say that “g of is .” This is equivalent to the ordered This is equivalent to the ordered pair pair Skill Practice Given the function defined by f (x) 2x 3 , find the function values. 6. f(1) 7. f(0) 8. f (3) 9. g1 10, 12, g102, g122, g142, 22 Notice that and correspond to the ordered pairs and In the graph, these points “line up.” The graph of all ordered pairs defined by this function is a line with a slope of and y-intercept of (Figure 2-33).This should not be surprising because the function defined by 12 g1x2 x 1 is equivalent to y x 1. 12 10, 12 12 112, 02, 14, 12, 2, 22. f a1 2 b 114, 12. 2, 22. 2 2 1 2 y 5 4 3 2 1 2 1 1 Answers 6. 5 7. 3 8. 3 9. 4 x 543 1 5 2 4 5 (4, 1) (2, 0) (0, 1) (2, 2) g(x) x 1 12 Figure 2-33
miller_intermediate_algebra_4e_ch1_3
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