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chapter 1 49

chapter 1 49 - CHAPTER 1 74 — 71 y— tanx —2 The graph...

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Unformatted text preview: CHAPTER 1 REVIEW 49 73. , 74. — 71 y— tanx —2 The graph of sin‘1 :2 is the reﬂection of the graph The graph of ‘can’1 m is the reﬂection of the of sin an about the line y = a3. graph of tan a: about the line y = x. 75. g(\$) 2 sin’1(3x +1). D0main(g)={m|—1£3x+1£1}:{m|—2§3m§0}:{x|—§Sw§0}: [7%.0]. Range(g)—{y| g3y:§}~[ea;l- 76. (a) f(1:) 2 sin(sin_1 x) (b) g(a:) : sin’1(sinm) . _ This is similar to part (a). but with domain IR. Equations for g on Since one function undoes what the other one does we get the intervals of the form (~% + 7m, g + 7m). for any integer n. can be identity function. y = :c. on the found using 9 (2:) : (~1)"x + (—1)”+1n7r. The sine function is restricted domain ~1 S x g 1. monotonic on each of these intervals. and hence. so is 9 (but in a linear fashion). 1 Review \ CONCEPT CHECK \ 1. (a) A function f is a rule that assigns to each element x in a set A exactly one element. called ﬂat). in a set B. The set A is called the domain of the function. The range of f is the set of all possible values of f(.1;) as :v varies throughout the domain. (b) If f is a function with domain A. then its graph is the set of ordered pairs {(m f(x)) [ :c E A}. (c) Use the Vertical Line Test on page 17. 2. The four ways to represent a function are: verbally. numerically. visually. and algebraically. An example of each is given below. Verbally: An assignment of students to chairs in a classroom (a description in words) Numerically: A tax table that assigns an amount of tax to an income (a table of values) Visually: A graphical history of the Dow Jones average (a graph) Algebraically: A relationship between distance, rate. and time: d : rt (an explicit formula) ...
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