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Unformatted text preview: 1.3 More on Functions and Their Graphs:
Increasing and Decreasing function: Increasing, Managing, an! Camstain 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,
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fix lawnusing [: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 Xcoordinates and not the y
coordinates. Where a function is positive, negative, and zero? Positive: A function is positive at a point on the Xaxis where
the graph of the function lies above the Xaxis (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 xaxis (formal deﬁnition: The set {x 1 f(x) < o}den0tes where f is negative). Zero: A function is zero at a point on the Xaxis where the graph
of the function lies on the Xaxis (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
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IIIIIIIII (—02» 2) WWW"? ND Cow—P Relative Maxima and Relative Minima: ﬂeﬁaiﬁnae at” Relative Maximum anti Relative Minimum 1. A irritation value fitI} 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 minim
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 xaxis
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 Xaxis
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]
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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.
 Fall '11
 BlisinHestiyas

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