This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 vr
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 112).  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 8an aﬁj
Lat f(x)=7_3=ﬁ_‘ r n
a)'Findthg(domain of f. 366311 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 Fal05 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. ‘ZcquA (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 (QMLQfMPD)
c) Find the intervals on which f is increasing, is decreasing, or is constant.  Q
‘tnwa QuizL443 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'cueirﬁ~ £013 2 L3(a+rb2+§(a+h) 1] —7 {:90} +397";
h “_“_’_#HF—H:ZT_‘_“‘_W__HH'
«2 Q (aZ—EZalntlnljrt BCOUElﬂ «#7 ﬁglaa— 3a +7. LloJchiql—(a  
‘2‘ u—ﬁr h Zbgm€§2hfaj ‘zJLfaQJLME‘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 ...
View
Full
Document
This note was uploaded on 04/25/2008 for the course MATH 30191 taught by Professor Terry during the Spring '08 term at Montgomery.
 Spring '08
 Terry

Click to edit the document details