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Week 1 - l if 5 l'20,” Chapter 3 Functions The Definition...

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Unformatted text preview: l if! 5 l '20,” Chapter 3: Functions. The Definition ofa Function [3.1] Let A and B be non—empty sets. A functidn from set A to B is a tule of correspondence that assigns to each in set A exactly one element in set B. W“ SetB WI Example-s: (if) SetA “m,ng 0V Pet Weight (lbs) 'i ' Every element in set A has I Exactly one element in B fails for one element in set B but Ford has no assignment the car and the pet's ht example. ' flu...“ __,5_ The setA o in u . called a the function, and the set B o -' 8 called range For example, for a equation y = ——5x + 1, .5- (0 —H :- ~5+l 24+- FSO—l‘) “H ‘1‘; 5+l‘T-‘(a “5(1) +l "-1 *“ lU‘lnl :.~‘? '- Graph x consists of domain values, A ll 3 y consists of the range values A 6 Following are the examples of what can or can’t be a domain value Find the domain of the following function: I N "lb 61 U0 [‘0‘ Ex1:y= 1 I, D$lUf0Uva 56 Exam Interval notation: “‘06 "V6 ' \ . "'1! (E w] #4) U (“4‘ «A “ . ‘ ' 3th: EN) deludefi, U :uhl‘m \6 set notation: EL é ‘ l ' \/~7]~'2,0H » ' Ex2: y=\/;°Jt+12, I I t ,5 3 YOOJr($&LMJLQ Mot) I 4‘M’Y’00t‘9’rc) *E 7/”?L ' “\ W‘W Wt Pith 1mg w m. WWthw/t W twat: 7 Ef‘fi (Sadr ‘ . I \M HM). Mwain Set notation: I it 9 n2 \ t 241} EXB: y_=\/33r+12, ‘ M saws G“) 003 1 .Exé: y=g(r)=t2_7t+12 I :I O M mart b3 )uq (qumbfi ):O “00% I 3 w ‘ WI. ‘ Interval notation: _ I U (3) U )co _ it e— In \ t % 3 SC *4} ‘ * w??? The graph of a function [3.2) Definition: The graph of a function f in the X-y plane consists of all those points (x, y] such that x is in the domain, and y = _f[x) i ' - How do you tell if a graph off rep sents a function? Vertical Line Test: A graph in the x-y plane represents y as a function of X if. any vertical _‘ line intersects the graph in at most one point. Find if the following graphs represent a function. Justify your answer. Then find the ' ction. 3.2 The Graph of a Function In Exercises 5 and 6, use the vertical line rest to determine 4' Spam, the y_wordmate ofthe POI-m P on [he wheiher each graph represents a fimcrion of x. : .fimcz‘ion. In each case, give an exact expres- iieror approximation rounded to three decimal p g 7 i 3 In Exercises 7—14, Ihe graph ofa function is given. In each case, specify the domain and the mnge ofthe function. (The axes are “fin-#— _ I _ marked ofi‘m one-um: Intervals.) 154 Chapter 3 Functions ; " . 15. (a) FindF(-5) " \ U (h) Find F(2). ' ‘f- 5 if) D i (c) Is F0) positive? : (d) For which value of x is F(x) = “3? i ’ (e) Find F(2)—F(—2). 16. (2} Find 17(4). (1)) Find H-l). (c) 15 F(*~4)7positive?' n . (d) For which value ofx is Rx) = 5? “'2 ) (e) Find F(5) — F{—3). ' + «3:33.? E? $4 v_..d.......m.. .zjr ' q Piecewise defined function: Look at $171? graphs 5—14, pg 153-154 n your text book. 3:0 ) 5:] ...
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This note was uploaded on 02/08/2011 for the course MATH 3 taught by Professor Staff during the Winter '08 term at UCSC.

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Week 1 - l if 5 l'20,” Chapter 3 Functions The Definition...

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