1.3(ONE) - 1.3 More on Functions and Their Graphs:...

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Unformatted text preview: 1.3 More on Functions and Their Graphs: Increasing and Decreasing function: Increasing, Managing, an! Cam-stain Flint-{loss i. a fanning: is increasing m1 as apes internal, I, if ani' may 3:, ans 3;; is [lac i§.1£ea'v&l,n=‘§1rir A: ~-: .r_s,.ilzm_;‘€x,& -: 3an, .2. Manning]. isfierrcasiagmianopeniii-156ml,Liffmrany}; Eiliaiireiliiiitflilliii’i'aidlill.t*i'fi .i‘uiilfll if, :ng 3. a {iiiiflilmi ismnsiaaienan ripen inlelvnijjfi'm’anger, :1fld3’;lt1 the interval,wheres; Ir: ,t;,3lienfr,} fungi, Illnesseng {Managing {Seminar 5 fi' IL 11'; in: .1". «z xlin I, [2} Filifl’.‘ mail. {3; {1mg vagina" gt, a, _l e: six-32;. fir; l :s {mg-J: {1; iii! 7 I"! nil: fix lawn-using [:21 l. V? i¥-tl:?§‘liiii‘ll-’§i_-E in] 1' {is smusiunim I, The open intervals describing where functions increase, decrease, or are constant, use X-coordinates and not the y- coordinates. Where a function is positive, negative, and zero? Positive: A function is positive at a point on the X-axis where the graph of the function lies above the X-axis (formal definition: The set {x | f(x) > 0} denotes where f is positive). Negative: A function is negative at a point on the x~axis where the graph of the function lies below the x-axis (formal definition: The set {x 1 f(x) < o}den0tes where f is negative). Zero: A function is zero at a point on the X-axis where the graph of the function lies on the X-axis (formal definition: The set {x 1 f(x) = 0} denotes where f is zero). Find Where the graph is increasing? Where is it decreasing? Where is it constant? 4'00 llflllllflll Ilflllllflll =--::=:::: i unlu- Inn-unl- III-null.- IIIIIIIII (—02» 2-) WWW"? ND Cow—P- Relative Maxima and Relative Minima: flefiaifinae at” Relative Maximum anti Relative Minimum 1. A irritation value fit-I} is a relative mania 3r mum of f if there exiais an ripest]: l]Eii‘-I’.‘Wfil about: at ranch that it a} fire fir: int all; a: in the open it: tearvaL A inaction value {iii} is a lili‘iflziit’fi mini-m mum at f if there estate an ape 3:1 interval alum: t2 snail that fight} *2: fits) tor ail A? in the 4.}53621 in larval. gelatin maximum Rfilflfiffi _ A“ minimum i‘l :1“ if 6 . x \ i E {i {i ifJ.,t{i1_.Iil Local Maximum: A local maximum occurs at an x-axis point where a graph peaks. (formal definition: A function f has a local maximum on an open interval containing a point c if f(x) 5 f(c) for all points X in the interval.) The local maximum is the value (output) of the function at this pomt. Local Minimum: A local minimum occurs at an X-axis point Where the graph dips lowest. (formal definition: A function f has a local minimum on an open interval containing a point e if f(X) 2 f(c) for all points X in the interval.) The local minimum is the value (output) of the function at this point. Find Where the graph is increasing? Where is it decreasing? Where is it constant? Where are the relative minimums? Where are the relative maximums? Why are the maximums and minimums called relative] 0_1_'_l9_§al? ...
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This note was uploaded on 01/16/2012 for the course MATH 126 taught by Professor Blisinhestiyas during the Fall '11 term at Truckee Meadows Community College.

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1.3(ONE) - 1.3 More on Functions and Their Graphs:...

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