Section%202.4

# Section%202.4 - . I3 Pope‘s“ / MA 180 ~ Precalculus '5...

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Unformatted text preview: . I3 Pope‘s“ / MA 180 ~ Precalculus '5 03/ Professor Terry - Section 2.4: Deﬁnition of Function E Functions Definition: A function f from a set D to a set E is a correspondence that assigns to each element x of D exactly one element y of E. “To {0.0% x m'fD ’WWC Coweefxmcls Qxadr/Qu) (one D \ tj m' E- «27% 2‘wn&ww\$ GALA girm :b “JELO E ave ozﬁuaﬂ {Or-=3 Poo/v e \$00:ng ¥wx€vzk\(%j From geometry, the volume of a region within a sphere is given by V = 13,, lTiFB. This equation deﬁnes a correspondence between two variables, r and V r __, v a a _ Li “(0') -=-_ O Exec; 0 MW 0—» __ I; 3 2% ﬁt L‘Ilﬂgc/awm 1————> at .i (0 eff 3 "— \ 2—» Efﬁe) siegfl at; 33.903) The volume is ag Lt martian. The gum/Q10": is a rule that assigns one V value to each r value, y = 5x + 7 also defines a function, for every x value, there is one y value. (6:550rri x~—>y , 0*~—> 6003+? 11E v-r 1—» 607+“! 2 Nil -2——-> 502347: ‘70“? :l‘3’ Functions are named with letters, f is the most popular. If a function is named f, and the independent variable is x, then the function notation f(x) can be used instead of y. y=5x+7 becomes 820(3: bXtPT MA180 Sec2.4 FallOS ewt If f(x)=—x3—x2+3,ﬁnd f(-3), rm) and 11-2). - 3103) z «(#531— (—- 3)‘9+3 z -— (—a7>_ 01 + 5 2314+5=lg \$(0)-2-(o)3'—(0)Z+3 2 [a 9(4) 21— (*1)B”C”Z)2“t3 = ape“) -— Lt ~i 5 z 8-an aﬁj Lat f(x)=7_3=ﬁ_‘ r n a)'Findthg(domain of f. 36-6311 M X+3'>,-O M )(+3a£0 Definition of the Graph of a Function: The graph of a function f is the graph of the equation y = f (x) for x in the domain of f. mama—est Vertical Line Test: The graph of a set of points in a coordinate plane is the graph of a function if every vertical line intersects the graph in at most one point. Are the following graphs of functions? @w MA1BO SecZ.4 Fal|05 ewt For the graph of the function f sketched in the ﬁgure, determine a) the domain b) the range c) f (1) d) all x such that f(x)=1 e) all x such that f(x)>1 @umm’ [1 5:er For f(x)=\/l6—x2. 7' a) Sketch the graph of f. ‘Zcqu-A (9' q) U§?A£M head) b) Find the domain D and range R of fz: ' -— a . d 13% E a’m‘a‘e R [or “Cl (QMLQfM-PD) c) Find the intervals on which f is increasing, is decreasing, or is constant. - Q ‘tnwa Quiz-L443 ELtp] 9%ch (D—e 02v“ 6 as [0 t Lt 3 Difference Quotient pod h If a is a real number and h \$0, find ﬁat—111), for f(x)=2x2 +3gc—7. ‘pt'cu-eirﬁ~ £013 2 L3(a+rb2+§(a+h) -1] -—7 {:90} +397"; h “_“_’_#HF—H:ZT_‘_“‘_W__HH' «2 Q (aZ—EZaln-tlnljrt BCOUElﬂ «#7 ﬁglaa— 3a +7. LloJchiql—(a - - ‘2‘ u—ﬁr h Zbgm€§2hfaj ‘zJLfa-QJLME‘J‘ MA180 Sec2.4 Fall05 ewt =—a?42qh+h1 Linear Function Definition of a Linear Function: A function f is a linear function if f (x) =ax+b , where x is any real number and a and b are constants. For f(x)=—2x+3. a) Sketch the graph of f . 3' 5/31 0 '5 3A2 0 l l b) Find the domain D and range..,£i...0fwfi- ma; "Li? 00 : £63.] c) Find the intervals on which f is increasing, is decreasing, or is constant. Al Naif)— be Meat/lag? L (-430, rm , If a linear function satisﬁes the conditions f (-2) = 7 and f (4) = —2, find f (x). KPGDLVCJL Geri) {M 2. '7’“? 2 iii ‘2 fl. 3 —5 FEW} Girl) ‘0" a“ 1”“0‘4‘) 3 “f. Radioactive contamination It has been estimated that 1000 curies of a radioactive substance introduced at a point on the surface of the open sea would spread over an area of 40,000 km2 in 40 days. Assuming that the area covered by the radioactive substance is a linear function of time t and is always circular in shape, express the radius r of the contamination as a function of t. if C9 A: W1 Cﬁim Aitioeféo W; a“? AFC? @ AG“): ijwtb I 1409002 CLO-(Lo) I MA180 8802.4 Fall05 evvt ...
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## This note was uploaded on 04/25/2008 for the course MATH 30191 taught by Professor Terry during the Spring '08 term at Montgomery.

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Section%202.4 - . I3 Pope‘s“ / MA 180 ~ Precalculus '5...

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