Chapter Review 133 Local minimum (p. 91) A function f, defined on some interval I, has a local minimum at c if there is an open interval in I containing c so that f c f x , ( ) ( ) ≤ for all x in this open interval. The local minimum value is f c . ( ) Absolute maximum and absolute minimum (p. 91) Let f denote a function defined on some interval I. • If there is a number u in I for which f u f x ( ) ( ) ≥ for all x in I, then f has an absolute maximum at u, and the number f u( ) is the absolute maximum of f on I. • If there is a number v in I for which f v f x , ( ) ( ) ≤ for all x in I, then f has an absolute minimum at v, and the number f v( ) is the absolute minimum of f on I. Average rate of change of a function (pp. 93–94) The average rate of change of f from a to b is y x f b f a b a a b ( ) ( ) Δ Δ = − − ≠ Objectives Section You should be able to . . . Examples Review Exercises 2.1 1 Describe a relation (p. 61) 1 1 2 Determine whether a relation represents a function (p. 63) 2–5 2–5 3 Use function notation; find the value of a function (p. 65) 6, 7 6–8, 43 4 Find the difference quotient of a function (p. 68) 8 18 5 Find the domain of a function defined by an equation (p. 69) 9, 10 9–14 6 Form the sum, difference, product, and quotient of two functions (p. 71) 11 15–17 2.2 1 Identify the graph of a function (p. 78) 1 31, 32 2 Obtain information from or about the graph of a function (p. 78) 2–4 19(a)–(e), 20(a), 20(e), 20(g) 2.3 1 Identify even and odd functions from a graph (p. 87) 1 20(f) 2 Identify even and odd functions from an equation (p. 88) 2 21–24 3 Use a graph to determine where a function is increasing, decreasing, or constant (p. 89) 3 20(b) 4 Use a graph to locate local maxima and local minima (p. 90) 4 20(c) 5 Use a graph to locate the absolute maximum and the absolute minimum (p. 91) 5 20(d) 6 Use a graphing utility to approximate local maxima and local minima and to determine where a function is increasing or decreasing (p. 93) 6 25, 26, 44(d), 45(b) 7 Find the average rate of change of a function (p. 93) 7, 8 27–30 2.4 1 Graph the functions listed in the library of functions (p. 100) 1, 2 33, 34 2 Analyze a piecewise-defined function (p. 105) 3–5 41, 42 2.5 1 Graph functions using vertical and horizontal shifts (p. 112) 1–5,11–13 19(f), 35, 37–40 2 Graph functions using compressions and stretches (p. 115) 6–8,12 19(g), 36, 40 3 Graph functions using reflections about the x-axis and the y-axis (p. 117) 9,10,13 19(h), 36, 38, 40 2.6 1 Build and analyze functions (p. 126) 1–3 44, 45 Review Exercises 1. While shopping online for AA batteries, Masoud found that he could order a pack of 8 batteries for $6.30, a pack of 16 for $13.99, a pack of 20 for $12.32, or a pack of 24 for $13.99. Define a relation using number of batteries as input and price as output. (a) What are the domain and range of the relation? (b) Express the relation as a set of ordered pairs. (c) Express the relation as a mapping. (d) Express the relation as a graph. In Problems 2–5, find the domain and range of each relation. Then determine whether the relation represents a function. 2. 1, 0 , 2, 3 , 4, 0 ( ) ( ) ( ) { } − 3. 4, 1, 2,1, 4,2 ( ) ( ) ( ) { } − 4. x y 1 4 2 2 ( ) − + = 5. y x4 5 3 = − − −
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