Transcript
A Tour of Your Textbook *
8=6EI:
Chapter Opener
G
H^cZ;jcXi
• This two-page spread introduces what you will learn in the chapter. • The specific curriculum expectations that the chapter covers are listed. • The vocabulary lists contain the mathematical terms that are introduced and defined in the chapter.
^dch
Ig^\dcdbZig^X ;jcXi^dch
9ZhXg^WZ`Znegd
eZgi^Zhd[e Zg^dY^X[jcX gZVa"ldgaYV i^dchVg^h^c\[gdb eea^XVi^dch! \^kZcVcjb Zg^Xdg\gVe EgZY^Xi!WnZmigV ]^XVagZegZhZciV edaVi^c\!i]Z[j i^dc# bdYZaaZYj ijgZWZ]Vk^ h^c\VcjbZ djgd[VgZaVi^dc g^Xdg\gVe] [jcXi^dc# h]^e ^XVagZegZhZ ciVi^dcd[V eZg^dY^X BV`ZXdccZXi^dc hWZilZZci ]Zh^cZgVi^ \gVe]^c\i] dVcYi]Zh ZgZaVi^dch] ^cZ[jcXi^dc ^eWZilZZc XdggZhedcY Wn Vc\aZh[gdb ^c\h^cZgVi^dh!Y %°id (+%°VcYi ZÒc^c\ f x 2h^cx!VcY ]Z ZmeaV^c^c\l]ni i]^hgZaVi^dch]^eVhi] Z[jcXi^dc ]ZgZaVi^dch]^e^ H`ZiX]i]Z\gV hV[jcXi^dc e]d[f x 2 # h^cx YZ\gZZh!Vc YYZiZgb^cZVcY [dgVc\aZbZVhjgZhZm egZhhZY^c YZhXg^WZ^i BV`ZXdccZXi^dc h`ZnegdeZgi^Zh # h!i]gdj\]^ckZh WZilZZcX]Vc\ i^\Vi^dcl^i]iZX Zh^cVgZVa"ldga ]cdad\n! bdYZaaZYj Yh^ijVi^dci]Vi h^c\VeZg^d XVcWZ Y^X[jcXi^dcVcY XdggZhedcY igVch[dgbV ^c\\gVe]# i^dchd[i]Z 9ZiZgb^cZ!i]gd j\]^ckZhi^\ Vi^dcjh^c\ i]ZeVgVbZ iZX]cdad\n!i]Z iZgha!c!Vc Yd^c[jcXi^dch gdaZhd[ f x 2h^cx ^ci]Z[dgb c!VcYf x 2h^c f x 2a h^cx! xÄd !VcYYZhX iZgbhd[igV ch[dgbVi^dchdc g^WZi]ZhZgdaZh i]Z\gVe]d[f x ZmegZhhZY^cYZ\ ^c 2h^cxl^i gZZh# ]Vc\aZh H`ZiX]\gVe]hd [f x 2ah^cx!f WnVeean^c\ x 2h^cx igVch[dgbV c!VcYf x 2h^c i^dchidi]Z\gV i]ZYdbV^c xÄd e]d[f x 2 VcYgVc\Z h^cx!VcYhiViZ d[i]ZigVch [dgbZY[jc 8daaZXiYViVi]V Xi^dch# iXVcWZbd YZaaZYVhV ^ckZhi^\Vi^dcl^ h^cZ[jcXi^dc!i] i]VcYl^i]dji gdj\] jh^c\VkVg iZX]cdad\n ^Zind[idda ![gdbeg^bV h!dg[gdbh gnhdjgXZh! YViV# ZXdcYVgnhd jgXZh!VcY\gVe] i]Z >YZci^[neZg^dY ^XVcYh^cjh d^YVa[jcXi^dch! Vg^hZ[gdbgZVa"l ^cXajY dgaYVeea^XV i^dch^ckdak^c\e ^c\i]dhZi]Vi \^kZckVg^d jhgZegZhZc Zg^dY^Xe]Z iVi^dch!VcY cdbZcV! i]ZXdciZmieaVX ZmeaV^cVcn Zhdci]ZY gZhig^Xi^dchi]Vi dbV^cVcYg EdhZegdWaZbh Vc\Z# WVhZYdcVe ea^XVi^dch^ckdak hdakZi]ZhZVcY ^c\Vh^cZ[ di]ZghjX] jcXi^dc!Vc egdWaZbhWnjh \gVe]\ZcZ Y gViZYl^i]iZX] ^c\V\^kZc \gVe]dgV cdad\n[gdb ^ihZfjVi^dc# ViVWaZd[kVajZ hdg[gdb ''-
>ccVijgZ!bVc ni]^c\h[daadl V XnXaZdggZ\jaVg eViiZgc#HdbZ ZmVbeaZhVgZi ]Zg^hZVcY[Vaad [ i^YZh!i]Zg^h^c\ VcYhZii^c\d[ i]Z hjc!VcYi]Ze] VhZhd[i]Zbd dc# I]ZhZgZ\jaVge ViiZgchXVcWZ YZhXg^WZYVhe Zg^dY^XWZ]Vk^d jgh VcYbdYZaaZYjh ^c\Vh^cZ[jcX i^dc# >ci]^hX]VeiZg! ndjl^aaaZVgc ]dl id^YZci^[neZg^d Y^X[jcXi^dch!gZ aViZ X^gXaZh!i]Zh^cZ gVi^d!VcYi]Zh ^cZ [jcXi^dc!VcYXd ccZXih^cZ[jcX i^dch l^i]gZVa"l dgaYh^ijVi^dch#
KdXVWjaVgn Vbea^ijYZ XdiZgb^cVaV c\aZh
XnXaZ
^c^i^VaVgb eZg^dY eZg^dY^X[jc Xi^dc e]VhZh]^[i h^cZXjgkZ h^cZ[jcXi^d
c hiVcYVgYed h^i^dc iZgb^cVaVgb iZgb^cVaed ^ci jc^iX^gXaZ
FA 11 CH05.in
dd 228-229
''.
3/5/08 4:25:00 PM
Prerequisite Skills • The questions review key mathematical skills that are needed for success with the chapter. • The Chapter Problem is introduced. Questions related to the Chapter Problem are in the Connect and Apply sections of the exercises throughout the chapter and are identified by a Chapter Problem descriptor (box).
EgZgZfj^h^iZ
H`^aah
! &!% ! %!( YEV^gh !% ! '!( ! )!( ! ( gYZgZYeV^gh ( # (!% !VcY )! YgVcih4 ih# &!% ! '!( ! d[i]Z[djgfjV YZWni]Zed^c x, y ^cZVX] i]ZeViiZgcbV hd[Ved^ci cViZ dgY^ i]Zx"VcYy"Xd i]Zh^\chd[ -# L]ViVgZ # Xh Vi^dc gVi^ VX]igVch[dgb ^dchd[FjVY gZhjaih[gdbZ IgVch[dgbVi [jcXi^dci]Vi ]ZfjVYgVi^X ZfjVi^dc[dgi ^ihjelVgY# .#Lg^iZVc ' ^higVchaViZY)jc i]ZaZ[i# ]d[yx V I]Z\gVe ViZY*jc^ihid x' ^higVcha dgd[(# y [VXi WnV ]d[ Zgi^XVaan W I]Z\gVe Yi]Zc ' ^hhigZiX]ZYk [VXidgd['Vc ]d[yx Zgi^XVaanWnV & X I]Z\gVe ' ^hhigZiX]ZYk T! dlc# ]d[yx WnV[VXidgd[ ( VcY+jc^ihY Y I]Z\gVe hZYkZgi^XVaan ^iidi]Zg^\]i "Vm^h!XdbegZh igVchaViZY&jc ' ÄZXiZY^ci]Zx yx ^hgZ ]d[ gVWdaV# VgY# \gVe jel Z I]Z iZmd[ZVX]eV haViZY'jc^ih #AVWZai]ZkZg WdaV VcYi]ZcigVc eVgV d[ZVX] ' h`ZiX]V\gVe] X y'x [dgbVi^dchid ( ' &%# JhZigVch ' W y x & * ' ) [ y( x V yx T& x' Z y' ' yx
EadiDgYZgZ
i]Zd ,# V Eadi
Ig^\dcdbZi
gn
c\i]d[i]
iZgb^cZi]ZaZ
idYZ iVc\ZcigVi^d ^cZ!Xdh^cZ!dg jc^i#
&# JhZi]Zh
idi]ZcZVgZhi V
X
W
:
8
&*Xb
f -Xb
7
i]ZcZVgZhiY d[Vc\aZx!id W
)(bb x
I
x @
B
&*Xb
A
x &(Xb
Y
@
cZVgZhi ch^YZ!idi]Z ZVX]jc`cdl
J
?
ZdgZ ni]V\dgZVci] (# JhZi]ZE # iZci]d[Vjc^i V
X
H
+,bb
-b
*b
F
Z\gZZ#
Zi]ZbZVhjgZ
A
E
&%bb
;
9
'# 9ZiZgb^c V
'-
G p
)&
+' 6 c
W 9ZhXg^WZ
Y! Zh^YZ^cY^XViZ
Zi]ZaZc\i]d[
bidYZiZgb^c
X W
P
I
s
J ,#-bb
6
&'#(bb 11.6 cm
b
10.5 cm
H
(#+Xb
)#,Xb
8
7
Q
GVc\Z 9dbV^cVcY
ZbZci# cYgVc\ZhiVi VX]YdbV^cV Rqy+r bZVc^c\d[Z gVc\Zpy y'r 'r W pxRqx3 pyRq' Xi^dc# Y gVc\Z \Z[dgZVX][jc px Rr dbV^cVcYgVc ]ZY g^iZi I]Zc!l ZVX][jcXi^dc# ' ]d[ \gVe x W y &'# H`ZiX]V ' & + ( x 'x Y y V y ( ' ) X y' x
&&# Lg^iZi]Z
V YdbV^c
R
p
^dch ig^X:megZhh
^\dcdbZ
:kVajViZIg
^bVaeaVXZh# idg!id[djgYZX W Xdh&*
X iVc)* VaeaVXZh# id[djgYZX^b ^XViZY#GdjcY gV(% X iVcV![d gi]ZkVajZ^cY dc[d gV&% gZhh^ (, dgV & h^c 'V(% (![d ZVX]Zme W *XdhV![ T *# :kVajViZ )* [ ' V+% dhV-![dgV V h^cV![dg .% Z (X V ![dg &%h^c V'%
l^i]VXVaXjaV
)# :kVajViZ
V h^c*%
Y
h
9gVl6c\aZ
ZVX]Vc\aZ# igVXidgidYgVl W )* V (% [ &-% Z &*%
+# JhZVegd
cations 11 tions and Appli '(%B=GFunc
X YdbV^c
X .% \ '%%
WaZb 8]VeiZgEgd
h
hiZb ghiVcY^c\d[hn ZaYjhZVcjcYZ nhiZbh i]ZbZY^XVaÒ k^djgh#I]ZhZh BVcnXVgZZgh^c geZg^dY^XWZ]V idZkVajViZ jaVgeViiZgch!d hi^XiddahjhZY i]ViZm]^W^igZ\ c\h! Y^ci]ZY^V\cd d[i]Z]ZVgi!aj VcWdYnVc li]ZVXi^dch Zm^hi^ci]Z]jb ZZ]d l^aah ^X[jcXi^dch# eiZg!ndj ZYjh^c\eZg^dY i]Zb#>ci]^hX]V XVcWZbdYZaa ^XVa^bV\^c\ Vgbh!VcYbZY ZH`^aahB=G EgZgZfj^h^i
'(&
Y &'% ] ',%
PM 3/5/08 4:25:31
• 8]VeiZg*
dd 230-231 FA 11 CH05.in
vi MHR Functions and Applications 11 • A Tour of Your Textbook
FA 11 FM.indd 6
3/6/08 2:12:09 PM
Numbered Sections Lesson Opener
*#&
Lessons start with a photograph and short description of a real-world setting related to the mathematical concepts in the lesson.
Investigate
>ckZhi^\ViZ How can you identify a graph
These are step-by-step activities, leading you to build your own understanding of the new concepts of the lesson. Many of these activities can best be done by working in pairs or in small groups to share ideas.
DC NdjXVc\gVe]VfjVYgVi^
t
3/5/08 4:22:00 PM
dgb^c^bjb
BZi]dY&/DC V ;gdbi]Z\gVe]!f % '#
Ilddi]Zg kVajZhd[xi]Vi\^kZi]ZhV bZkVajZ d[fVgZx'VcYx' #
y 2 (0, 2) y = f(x)
W ;gdbi]Z\gVe]!f % #* %
#Ild di]ZgkVajZhd[xi]Vi\^kZ i]ZhVbZ kVajZd[fVgZx'#*VcY x&#*#
(0.5, 0) –2
–1
0
1
2
x
–1
X YdbV^cpxRr
–2
gVc\ZpyRq'y 'r
Key Concepts
1
@Zn8dcXZeih • 6eZg^dY^X[jcXi^dcgZeZVih^ihy "kVajZhVigZ\jaVg^ciZgkV ah# I]ZeZg^dYd[i]Z[jcXi^dc^hi]Z
aZc\i]d[dcZXnXaZ!bZVhj gZYVadc\i]Z]dg^odciVaVm ^h# XVaXjaViZYVhbVm^bjbkVajZb^c^bjbkV ajZ # '
• This feature summarizes the concepts learned in the lesson. • You can refer to this summary when you are studying or doing homework.
I]ZVbea^ijYZd[i]Z[jcXi^dc^h
TTTTTT
y
amplitude
0
x period
Communicate Your Understanding 8dbbjc^ '()B XViZNdjg =GFunctions JcYZghiV cY^c\ and Applica tions 11 • 8]VeiZ g* 8& 6eZghdc^hWdjcX^c\dcVigVbeda ^cZ#I]Z\gV
e]gZegZhZcihi]Z bZ#
h
]Z^\]id[i]ZeZghdcVWdkZi]Z\gdjcYdkZgi^
V :meaV^cl]ni]Z[jcXi^dc^heZg^dY
FA 11 CH05.indd 234
Height (m)
These questions allow you to reflect on the concepts of the section. By writing about or discussing these questions in a group, you can see whether you understand the main points and are ready to start the exercises.
^X#
W 9ZhXg^WZ]dlndjldjaYYZiZgb^c
Zi]ZeZg^dYd[i]Z[jcXi^dc#
X 9ZhXg^WZ]dlndjldjaYYZiZgb^c Zi]ZVbea^
4 2
ijYZd[i]Z
[jcXi^dc#
3/5/08 4:22:34 PM
0
4
8 12 Time (s)
t
8' 6lZ^\]idcVheg^c\^hWdjcX^c\j eVcYYdlc
# Z#
9ZhXg^WZi]Z\gVe]d[^ih]Z^\]igZaVi^kZidi^b
Practise A
'# 9ZiZgb^cZi]ZeZg^dY!Vbea^ijYZ!
YdbV^c! VcYgVc\Z[dgZVX]eZg^dY^X[jcXi^dc#
For help with questions 1 and 2, refer to Example 1.
Exercises
V
y
&# 9ZiZgb^cZl]Zi]ZgdgcdiZVX]\g
eZg^dY^X#?jhi^[nndjgYZX^h^dc#
V
2
Ve]^h –2
y
Practise A
0
–2
• These questions provide an opportunity to practise your knowledge and understanding of the new concept. • To help you, questions are referenced to the Examples.
0
2
jVi^dc[dgZVX]h^c W Z[jcXi^dc#
V y
&# H`ZiX]V\g
Ve]d[ZVX][jcXi ^dc[dg %x(+%#9Z iZgb^cZi]ZeZg^d Vbea^ijYZ!YdbV Y! ^c!VcYgVc\Z# & W yT h^cx ( X y'h^c x & Y yT h^cx ' V y+h^cx
'# 8dbeVgZi]
Z\gVe]hd[ZVX] eV^gd[ [jcXi^dch[dg% x(+%#9ZiZg eZg^dY!Vbea^ijY b^cZi]Z Z!YdbV^c!VcYgV lZaaVhi]ZZfjVi c\Z!Vh ^dcd[i]Z]dg^odc iVaVm^h# V yh^cx +VcYyh^cx + W yh^cx &#*VcYyh^cx &#* (# 8dbeVgZi] Z\gVe]hd[ZVX] eV^gd[ [jcXi^dch[dg% x(+%#9ZiZg eZg^dY!Vbea^ijY b^cZi]Z Z!e]VhZh]^[i!Yd VcYgVc\Z# bV^c!
Connect and Apply B
0
X =dlldjaY
i]Z\ W gVe]X]Vc\Z^[i] X^gXaZlVhbdkZY y Z [Vgi]Zg[gdbi]Zl hdi]Vii]ZXadhZhi Vaa ed^cilVh'#*b VlVaa4L]Vild [gdb jaYWZi]ZgZhjai4 ^c\ ZfjVi^dc4 Y =dlldjaY i]Z\gVe]X]Vc\ Z^[nd lVa`ZY^cVXadX` –4 0j 4 l^hZY^gZXi ^dc4L]Vi ldjaYWZi]ZgZhj ai^c\ZfjVi^dc4 –4 For help with questions 5 and 6, refer to Example 2. *# Lg^iZVcZf y
0
180°
360°
540°
0
+% VcYyh^c x+% ',% VcYyh^c x.%
90°
180°
• These questions allow you to use what you have learned to solve problems and make connections among concepts. In answering these questions you will be integrating your skills with many of the mathematical processes. • There are many opportunities to use technology. If specific tools are needed, these are noted and the question has a Use Technology descriptor. • Many sections include a Chapter Problem question and/or an Achievement Check question. *#)>ckZhi^\ViZIgV
4x
–4 x
x
1 (90°, 0)
0
180°
x
–1
Z8jgkZh B=G
'+'B=GFu
90°
3/5/08 4:26:36 PM
X 270°
180°
2
4
Y f x h^cx
B
x
y
nctions and Applic
'+&
261
X f x h^cx x
0
^cx
^cx
*
-
)*
[ f x h^c x .%
&%#L^i]dji\gV
e]^c\!Xdch^YZgZ VX]h^cZ [jcXi^dc#>YZci^ X [ni]ZeZg^dY!Vb ea^ijYZ! e]VhZh]^[i!YdbV x ^c!VcYgVc\Z!VhlZaa y –4 0 4 jVi^dc 8 i]ZZf Vh d[i]Z]dg^odciV aVm^h# 1 V yh^cx (–150°, 0) –4 (% W yh^c x (% &&# ;dgZVX]d[ –180° 0 i]Z[jcXi^dch!ÃcY 180° x i]Z XddgY^cViZhd[i] –8 –1 ZbVm^bjbVcYb ed^cih# ^c^bjb V yh^cx W yh^cx &' X y&%h^c Connect and x Y yh^c x Apply +% &'# V cY^XViZi]Z^ciZgk Vah^cl]^X]i]Z -#9gVlVh`Z ^h^cXgZVh^c\VcY [jcXi^dc iX]d[yh^c x YZXgZ .% Vh^c\ dcZeZg^dY# [dg dkZgd g^dY# *#&EZg^dY^X V Vbea^ijYZ;jcXi^dchBcZeZ &%!]dg^odciVaVm =G '(* V AdXViZVaai ^hVadc\ i]Zx"Vm^h ]Zed^cihl]ZgZy &VcY \^kZi]ZkVajZhd W Vbea^ijYZ [x# &!]dg^odciVaVm W AdXViZVaai ^hVad yc\ ]Zed^cihl]ZgZy %VcY \^kZi]ZkVajZhd X Vbea^ijYZ&!]d [x# g^odciVaVm^hVad x"Vm^h!e]VhZh]^[ c\i]Z id[)%idi]ZaZ[i 3/5/08 4:23:01 PM Y Vbea^ijYZ &!]dg^odciVaVm ^hVadc\i]Z x"Vm^h!e]VhZh]^[ id[&%%idi]Zg^ \]i
y
ch[dgbVi^dchd[H^c
FA 11 CH05.indd
270°
V f x %#)h
Z f x h^c x
0
2
0
–2
–2
y
kZhi^\ViZ7!^cl] –2 ^X]ndjlVa`ZY XdjciZgXadX`l^hZ ^cVX^gXaZ!WZ\^c ed^ciZfj^kVaZci c^c\ViV id(/%%dcVXadX` ndj\gVe]ZYi]Z #I]Zc! X gZhjaih# V =dlldjaY i]Vi\gVe]X]Vc\ Z^[ndj ^chiZVYWZ\VclV a`^c\[gdbi]ZaZ ed^cid[i]ZX^gX [ibdhi aZ4L]VildjaY WZi]Z gZhjai^c\ZfjVi^dc –180° 4 W =dlldjaY i]Z\gVe]X]Vc\ Z^[ndjg X^gXaZlVh'b^c gVY^jh4L]Vild FA 11 CH05.indd 235 WZi]ZgZhjai^c\Z jaY fjVi^dc4
nXaZd[ZVX][jcXi ^dc#AVWZa i]Zx"^ciZgXZeih! i]ZbVm^bjbed^ i]Zb^c^bjbed^ cih! cih!VcYi]ZZfj i]Z]dg^odciVaVm Vi^dcd[ ^h#Lg^iZi]ZYdb gVc\Zd[i]ZXnXa V^cVcY Z#
2
W f x )h
W
V yh^c x
)# GZ[Zgid>c
y = –3.5
y
W yh^c x
.#ckZhi^\ViZ
\gVe]^c\XVaXjaVidg
=dlXVcndjjhZZmedcZ ci^VagZ\gZhh^dcdcV\gV e]^c\XVaXjaVidg4 NdjXVcjhZi]ZZmedcZ ci^VagZ\gZhh^dc[jcXi^dc dcV\gVe]^c\ XVaXjaVidgid\ZcZgViZVc ZmedcZci^Va[jcXi^dci] VibViX]Zh\^kZcYViV# I]Z[jcXi^dc^hegZhZciZ Y^ci]Z[dgbyabx # &# V :ciZgi]Zi^bZVc YcjbWZgYViV[gdbHZX i^dc+#,fjZhi^dc&' ^cida^hihA&VcYA'#
• A TI-83 Plus or TI-84 Plus graphing calculator is useful for many sections.
EgZhh STAT #8jghdgdkZgid i]ZCALCbZcj# I]Zc!hZaZXi0:ExpReg# EgZhh 2nd &[dgA& ![daadlZYWn # EgZhh 2nd '[dgA' ![daadlZYWn # EgZhh VARS #8jghdg dkZgidi]ZY-VARS bZcj# HZaZXi1:Function!VcYe gZhh ENTER # HZaZXi1:Y1# EgZhh ENTER iddWiV^ ci]ZExpReghXgZZc# Lg^iZi]ZZfjVi^dcd[i] ZZmedcZci^Va[jcXi^dc^ cyabx[dgb# X JhZi]Zl^cYdl hZii^c\hVhh]dlc# EgZhh GRAPH # W
Y JhZi]ZTRACE
[jcXi^dcid^cheZXikVajZ h Vadc\i]Z\gVe]#9di]Zn bViX]i]ZkVajZh ^ci]ZiVWaZ4
(()B=GFunctions and
Applications 11 • 8]VeiZg+
FA 11 CH06.indd 334
&# ViZgi]Vc dcZ Via^h\gZ i]ZWajZ Zghdi] beVgZhid i]Zha^Y gVWdaVXd (#BdkZ ]ZgZYeV ^WZ]dli x' # &# )#9ZhXg cY y %V ^c\ lZZc gZegZhZci Via^hWZi WdaVh# Zghdi] WajZeVgV i]Zha^Y ZgZYVcY *#BdkZ dcigVhii] Vi^kZ# VgZVcYX ZgZY Via^hcZ\ +#8dbe VkZdci] %hdi] YdZha] a^YZgeVhi ZXi Zh Z[[ i] ,#BdkZ i^kZ!l]Vi bZhcZ\V aWZXd -#L]Zc ]# dgi ' # VcY[ eVgVWdaV4 ZgWVX` yax i]Zha^Y [jcXi^dc %# anbdkZ fjVYgVi^X &!VcYa .#Hadl [a^ci]Z a&!% a ZgdaZd hZl]Zc hXg^WZi] &%#9Z djggZhedc 6YYgZhhn y h ' ^h(i^bZ 12 y(x y = 3x² \gVe]d[ dcY^c\ cidci]Z ZXdggZhe 10 :kZgned^ ]Zx"Vm^hVhi] ' ]Z\gVe]d[ #I bi d[yx Vh[Vg[gd rtical 8 i]Z\gVe] # VaaZYVve ed^cidc &!^hX ' WnV[VXidgd[a ' !l]ZgZa x ax y ]d[y y = x² 6 [i]Z\gVe stretchd 4 2
–4
–2
0
3/5/08 4:31:01 PM
(2, 12)
• Fathom™ and The Geometer’s Sketchpad® are used in several sections for investigating concepts related to quadratic functions and trigonometry. Alternative steps for doing investigations using pencil and paper are provided for those who do not have access to this computer software.
stretch
l iX]WnV ^XVahigZ ! VkZgi gZa& [a!l]Z [VXidgd gned^ci ]ViZkZ h bZVchi i^bZhV gVe]^ha ]Z dci]Z\ Vhi m^h i]Zx"V i]Z [Vg[gdb ed^cidc ^c\ dcY XdggZhe ' y2x ]d[ 4) \gVe (2, jZ!i]Z X]x"kVa [dgZV a^ZYWna ^hbjai^e (1, 3) y"kVajZ eeZVgh gVWdaVV daV i]ZeV ]ZeVgVW (1, 1) gi]Vci cVggdlZ ' VajZd[a 4x Vhi]Zk x 2 y2 [dg gdb& ^cXgZVhZh[ vertica
=G ((
Xi^dch B
]Zhd[;jc
&#)HigZiX
3/5/08
4:19:28
I]^hegdeZginXVcVahdWZ jhZY^ch^ijVi^dch^ckda k^c\i]ZegdYjXid[ild W^cdb^Vah#
PM
{ ab cd
Distribute (a + b) into
ab c ab d acbcadbd
.indd 33
FA 11 CH01
Distribute c into (a +
the second binomial.
b) and d into (a + b).
:mVbeaZ&Simplif y Quadra
tic Expressions
:meVcYVcYh^bea^[n# V y( y* W 'n( ' X (k) k& k( '
• Some sections require a computer algebra system (CAS) to explore algebraic processes or as an alternative tool to solve algebraic problems. This text uses the TI-89 calculator.
HDAJI>DC V y( y*
BZi]dY&/JhZ6a\ZWgVI ^aZh 8dchigjXiVgZXiVc\aZ]V k^c\l^Yi] y(VcYaZc\i]y*# JhZ&y'"i^aZ!-y"i^aZh!Vc Y&*jc^ii^aZhid gZegZhZcii]ZVgZVd[i]^h gZXiVc\aZ# I]ZgZ[dgZ! y( y* y'-y&*# BZi]dY'/JhZi]Z9^hig ^Wji^kZEgdeZgin y( y* y( y y( * Multiply y + 3 by y and by 5. y'(y*y&* y'-y&* 8]ZX`/JhZV8dbejiZg6a \ZWgVHnhiZb 86H idkZg ^[ni]ZVchlZg# EgZhh F2 (# EgZhh
(
Y
+
(
)
(
Y
+
*
)
)
ENTER #
Technology Tip
When using a TI-89 calculator, a second closing parenthesis is required for expanding expressions.
'#'FjVYgVi^X;jcXi^dch/8db
eVg^c\;dgbh B=G ,.
FA 11 CH02.indd 79
Technology Tip
3/5/08 4:39:55 PM
This margin feature points out helpful hints or alternative strategies for working with specific technology. Technology Appendix
The Technology Appendix provides detailed help with all the functions of the graphing calculators, Fathom™, and The Geometer’s Sketchpad® that are used in this course. A Tour of Your Textbook • MHR ix
FA 11 FM.indd 9
3/6/08 2:12:26 PM
Assessment
8dbbjc^XViZNdjgJ
cYZghiVcY^c\
8& 8denVcYXdbeaZi
Zi]ZiVWaZh]dl^c\i]Zh^ \cd[ZVX]d[i]Zig^\dcdb VgdjcYi]Zjc^iX^gXaZ# Zig^XgVi^dhVhVgdiViZh ;^ghiFjVYgVci
Communicate Your Understanding
y 1
HZXdcYFjVYgVci
–1
I]^gYFjVYgVci
y P(x, y) 1
P(x, y)
1x
0
–1
–1
;djgi]FjVYgVci
y 1
y 1
1x
0
–1
–1
1x
0
–1
P(x, y) –1
1x
0 –1
P(x, y)
H^\cd[XdhV
• These questions provide an opportunity to assess your understanding of the concepts before proceeding to use your skills in the Practise, Connect and Apply, and Extend questions. • By working through or discussing these questions, you can identify any concepts you need to study further.
H^\cd[h^cV H^\cd[iVcV 8' JhZXdiZgb^cVaV
c\aZhid]ZaeZmeaV^cl]n
i]ZkVajZhd[h^cVVgZeZg
^dY^X#
Practise A
For help with question
For help with question s 1 and 2, refer to Example 1.
V .%
W )*
Y %
X -(
Z &(%
[ &-%
] '.)
2.
cYVgYedh^i^dcVcY ]VhiZgb^cVaed^ciE#;dgZ VX]hZid[ XddgY^cViZh[dgE!ÃcYi]Z gVY^jhd[i]Z X^gXaZ^cZmVXi[dgbVcYi] ZbZVhjgZd[ i]ZVc\aZidi]ZcZVgZhiiZc i]d[VYZ\gZZ# >cXajYZVY^V\gVb^aajhigVi ^c\ZVX]Vc\aZ# V E *!&' W E )!( X E +!. Y E ,!'
VaVc\aZh[dgZVX] \^kZcVc\aZ#9gVlZVX]hZi d[XdiZgb^cVa Vc\aZhdci]ZhVbZhZid[V mZh^chiVcYVgY edh^i^dc#
\ '%*
3, refer to Example
(#6cVc\aZ^h^chiV
&# ;^cYildXdiZgb^c
For help with question s 4 to 7, refer to Example 3.
^ (&%
'#L]^X]eV^ghd[Vc
\aZhVgZXdiZgb^cVa4 ?jhi^[nndjgVchlZg# V (%VcY'&% W ,%VcY)(%
)# ;^cYi]ZXddgY^c
ViZhd[ViZgb^cVaed^ci! E x, y ![dgZVX]Vc\aZ ^chiVcYVgYedh^i^dc dci]Zjc^iX^gXaZ#GdjcYid dcZYZX^bVa eaVXZ#9gVlVY^V\gVbid^ aajhigViZZVX] Vc\aZ#
X &%%VcY-'% Y (-%VcY+-%
V +)
Z )%VcY('%
W .%
Y (%%
[ *%VcY)%%
X &*%
Z ')%
[ &-%
*#'8^gXaZhVcYi]ZH ^cZGVi^d B=G
')*
FA 11 CH05.indd 245
3/5/08 4:26:10 PM
&&# I]ZHe^cc^c\L]ZZ
ag^YZViVadXVa[V^g^h VaVg\ZkZgi^XVal]ZZai]Vigdi ViZhVgdjcYV hiVi^dcVgnVm^h#I]ZiVWaZh]d lhi]Z]Z^\]i! ^cbZigZh!VWdkZi]Z\gdjcY d[VeZghdc g^Y^c\i]ZHe^cc^c\L]ZZa#
Special Connect and Apply Questions
I^bZ h
=Z^\]i b
%
&#*
'
• Some questions are related to the Chapter Problem. These are identified by a descriptor. • Achievement Check: The last Connect and Apply question of some sections provides an opportunity to demonstrate your knowledge and understanding and your ability to apply, think about, and communicate what you have learned. Achievement Check questions occur every two or three sections and are designed to assess learning of the key concepts in those sections. • For some questions it is suggested that you use the Internet to help solve the problem or to research or collect information. Some direct links are provided on our Web site www.mcgrawhill.ca/functionsapplications11.
6X]^ZkZbZci8]ZX` &'# 6X]^aY^hhl^c\^c\
dc Vhl^c\^ci]ZeVg`#I]Z l^Yi]d[]Zghl^c\e Vi]^h )bVcYdcZhl^c\WVX` VcY[dgi]iV`ZhVWdji'h#
V 9gVlV\gVe]i]Vi
)#'
)
)#* '#( &#*
&'
W :meaV^cl]ni]Zhl
eZg^dY^X[jcXi^dc#
'%
fj^ebZciVahd]VkZ VeZg^dY^XXdbedcZci#:meaV^ c]dlV eZg^dY^X[jcXi^dcgZaViZhidV iZZiZg"idiiZg!VbZggn"\d"gdjc Y!dgVhZi d[bdc`ZnWVgh#
&#*
''
)#'
')
Extend
+#-
C
V BV`ZVhXViiZgeadi
d[i]ZYViV#
W 9di]ZYViVVeeZVg
&(# 7Vh^a^hdcVaVg\ZkZ
idWZeZg^dY^X4
:meaV^c#
\cdiWZ
eZg^dY^X4
Y Di]ZgeaVn\gdjcYZ
+#)#* '#(
^c\»hbdi^dc^hV
X L]Zcb^\]iVX]^aY »hhl^c\^c
)#'
&) &+ &-
)b
gZegZhZcihi]ZY^hiVcXZ [gdbgZhiV[iZgthZXdcYh#
+#-
+ &%
X 9gVlVXjgkZd[WZh
iÃiVcYZmiZcY^i[dg VcZci^gZg^YZi]ViaVhih&b^c # Y L]Vi^hi]ZY^[[ZgZc XZWZilZZci]Z bVm^bjbVcYi]Zb ^c^bjb]Z^\]i gZVX]ZYYjg^c\i]Zg^YZ4
gi^XVahe^cc^c\l]ZZa ViVcVbjhZbZcieVg`#=ZhiV gih]^hg^YZVi i]ZadlZhied^ci!l]^X]^h(b VWdkZi]Z \gdjcY#I]ZgVY^jhd[i]Z;Z gg^hl]ZZa^h ,b!VcY^i^hgdiVi^c\Vi'#*g Zkdaji^dcheZg b^cjiZ#H`ZiX]V\gVe]gZegZ hZci^c\7Vh^a»h ]Z^\]iVWdkZi]Z\gdjcY!gZaVi ^kZidi^bZ! [dgV'"b^cg^YZ#
Career Connection 7Zii^cVXdbeaZiZYVi]g ZZ"nZVgYZ\gZZ ^cZVgi]VcYVibdhe]Zg^ XhX^ZcXZhVi VcDciVg^djc^kZgh^inVc Yi]ZclZci dcidVX]^ZkZ]ZgbVhiZ gÉhYZ\gZZ^c dXZVcd\gVe]n#>c]ZgXV gZZgVhVe]nh^XVa dXZVcd\gVe]Zg!7Zii^cV hijY^ZhXjggZcih! i^YZh!VcYlVkZh!VcY]d li]Zn^ciZgVXi l^i]i]ZVibdhe]ZgZ#H] ZXdaaZXih! VcVanhZh!VcY^ciZgegZih YViVdci]Z iZbeZgVijgZd[i]ZlViZ g!i]ZVbdjci
d[hVai!VcY]dla^\]iVc YhdjcYigVkZa ^clVkZeViiZgch#I]^h^ c[dgbVi^dc XVcWZjhZYidWj^aYVX dbejiZgbdYZa d[VcdXZVcXa^bViZ!l] ^X]]Zaeh bZiZdgdad\^hihidegZY^ Xii]ZlZVi]Zg# 7Zii^cVÉhYViVVahdXVcW ZjhZYidÒcY dji]dlhZVaZkZah]VkZ X]Vc\ZYdkZg i^bZVcY^[i]ZhZX]Vc\ Zhb^\]iedhZ VcZck^gdcbZciVa]VoVgY #
'(-B=GFunctions and Application
s 11 • 8]VeiZg*
FA 11 CH05.indd 238
3/5/08 4:24:12 PM
Chapter 5 Rev
iew
*#&EZg^dY^X;jc
Xi^dch!eV\Zh'(
&# 9ZiZgb^cZ
'Å'(-
*#'8^gXaZhVcY i]ZH^cZGVi^d! eV\Zh'(.Å'),
l]Zi]ZgdgcdiZV X]\gVe]^h eZg^dY^X#>[^i^h! YZiZgb^cZi] ZeZg^dY! Vbea^ijYZ!YdbV ^c!VcYgVc\Z#
(#6cVc\aZ^h
^chiVcYVgYedh^i ^dcl^i]^ih iZgb^cVaed^ci!E !\^kZc#;^cYi]Z i]ZX^gXaZ^cZmVXi gVY^jhd[ [dgbVcYi]ZbZ i]ZVc\aZidi]Zc VhjgZd[ ZVgZhiiZci]d[VY Z\gZZ# W E &'!* X E ,!- Y E '!& )# 6iZgb ^cVaed^ci!E x, y !dci]Zjc^iX^ [dgbhi]Z\^kZcV gXaZ c\aZ^chiVcYVgY ;^cYi]ZXddgY^c edh^i^dc# ViZhd[ed^ciE!id YZX^bVaeaVXZh# i]gZZ V +% W &(* X &-% Y &++ Z '.% [ ('%
V
Chapter Problem Wrap-Up
y 40 20 –2
0
2
4
–20
This summary problem occurs at the end of the Chapter Review. The Chapter Problem may be assigned as a project.
W
6 x
y 4 2
0
5
–2
10
15 x
g^hZVcY[VaaVih^ iZhVgdjcY i]ZldgaY#I]Zi VWaZh]dlhi]ZY lViZgVidcZadXV Zei]d[ i^dc[dgV'"YVne Zg^dY# I^bZ
9Zei] b
(/)'
(#&+adli^YZ
./)-
&'#&(]^\]i^YZ
&+/&)
'#-*adli^YZ
''/&,
&'#%&]^\]i^YZ
)/(-
'#.%adli^YZ
&%/)%
&'#(']^\]i^YZ
&,/%)
'#+&adli^YZ &'#(']^\]i^YZ
V H`ZiX]Vi^b
Z\gVe]d[i]Zi^Y ZYZei]h# ZeZg^dYVcYi]Z Vbea^ijYZ d[i]Zi^YZXnXaZ# X :hi^bViZi] ZbZVcYZei]d[ i]ZlViZg# W :hi^bViZi]
'+-B=GFu
nctions and Applic
FA 11 CH05.indd
jVi^dc[dgZVX]h^c Z[jcXi^dc#
V
-# JhZIZX]cd
0
180°
360°
–1
540° x y = –1
–2
W
y 2
0
*#(>ckZhi^\ViZ i]ZH^cZ;jcXi^ eV\Zh')-Å'*( dc!
ations • 8]VeiZ
cYaZ^hjhZYidZm iZcYVcY gZigVXiVcVlc^c \#I]ZgVY^jhd[i] XgVc`]VcYaZ^h& Z jc^iVcYi]ZY^gZ gdiViZh^hXdjciZg Xi^dc^i XadX`l^hZhiVgi^c ]dg^odciVaedh^i^ \[gdbV dc#GdjcYVchl cZVgZhiiZci]d[ Zghidi]Z Vjc^il]ZccZXZ hhVgn# V L]Vi^hi]Z ]Z^\]id[i]Z]Vc YaZV[iZg^i gdiViZh+%4 W L]Vi^hi]Z ]Z^\]id[i]Z]Vc YaZV[iZg^i gdiViZh&-%4 X L]Vi^hi]Z ]Z^\]id[i]Z]Vc YaZV[iZg^i gdiViZh'%%%4 Y ;^cYildg diVi^dcVaVc\aZhV il]^X]i]Z ]VcYaZ]Vh]Z^\] id[%#*jc^ih#
*#)>ckZhi^\ViZ IgVch[dgbVi^dc 8jgkZh!eV\Zh'* hd[H^cZ )Å'+( Ve]d[ZVX][jcXi ^dc[dgdcZ XnXaZ#9ZiZgb^cZ i]ZeZg^dY!Vbe e]VhZh]^[i!YdbV a^ijYZ! ^c!gVc\Z!VcYi] ZfjVi^dcd[i]Z] Z dg^odciVaVm^h# V y*h^cx & W yT h^cx ) X yh^cx &' Y yh^ cx '#* Z yh^c x +% [ yh^ c x.%
+#H`ZiX]V\g
g*
268-269
*#*BV`Z8dccZ Xi^dchL^i]H^c eV\Zh'+)Å'+, Z;jcXi^dch!
y 1
90°
–2
180°
270°
x
*# 6XgVc`]V
'#DXZVci^YZh
'(/%*
,#Lg^iZVcZf
V E )!(
ad\n6 W^dg]ni]bi]Zdg XXdgY^c\idi]Z n!i]gZZXnXaZhV[ eZdeaZ»ha^kZh!\^k [ZXi ^c\i]Zb[VkdjgV cdc"[VkdjgVWaZY WaZVcY Vnh#I]Ze]nh^XVa XnXaZ XVcWZbd YZaaZYVhy (+% h^c T t !l]ZgZt gZegZhZcih '( VeZghdc»hV \Z!^cYVnh# H^b^aVgan!i]ZZb di^dcVaXnXaZXVc WZ bdYZaaZY .% Vhyh^c T t VcYi]Z , ^ciZaaZXijV aXnXaZVhy &'% h^c T t #JhZV \gVe]^c\XVaXj && aVidg XnXaZh[dg%t idXdbeVgZi]Zi]gZZ +%#
.#JhZIZX]cd
X
ad\nI]Z]Z^\]id [Vg^YZgdcV ;Zgg^hl]ZZa!^cb ZigZh!XVcWZbdY jh^c\i]Z[jcXi^dc ZaaZY h V &%h^c V.% &'! l]ZgZV^hi]ZVc \aZd[gdiVi^dc#
y 1
0
(45°, 0)
V JhZV\gVe]
90°
–1
180°
270°
x
^c\XVaXjaVidgid
[jcXi^dc#
\gVe]i]Z
W L]Vi^hi]Z
gVY^jhd[i]Z;Zgg
^hl]ZZa4 l]Zci]Z
X 6il]Vi]Z^
g^YZWZ\Vc4
\]ilVhi]Zg^YZg
Y =dlldjaY
i]Z[jcXi^dc VcYi]Z\gV X]Vc\Z^[i]Z;Zgg ^hl]ZZaijgcZY e] deedh^iZY^gZXi^d ^ci]Z c4
Chapter Pro
blem Wrap-Up
JaigVhdjcY^hVb ZY^XVa^bV\^c\iZ 6bZY^XVa^bV\^ X]c^fjZi]Vi]VhW c\iZX]c^X^VcjhZh di]Y^V\cdhi^XVc WZYZÃcZYWni]Z VcjaigVhdjcYbV Yi]ZgVeZji^XVee ZfjVi^dcI t * X]^cZdcVeVi^Zc a^XVi^dch# ^ccVcdLViih cL h^c &&%%%%%t i#I]Zh^\cVaegdY !VcYtgZegZhZcih '( !l]ZgZI t gZe jXZYXVc i]Zi^bZ!^chZXdc gZhZcihi]ZhdjcY V L^i]i]Z]Z Yh# gVY^Vi^dc! aed[V\gVe]^c\X VaXjaVidg!h`ZiX]V W L]Vi^hi]Z \gVe]d[i]^hgZaV bVm^bjbVcYb i^dc[dg%t% ^c^bjbgVY^Vi^dc #%%%,# X L]Vi^hi]Z egdY jXZY Wni]^hjaigVhdjc eZg^dYd[i]Zhd YbVX]^cZ4 jcYgVY^Vi^dc4= Y =dlYdZh dlbVcnXnXaZh i]^h\gVe]Xdbe dXXjg^c&h4 VgZidVlVkZl^ i]ZfjVi^dcI t Z I]ZiZX]c^ X^VcVY_jhihi]Zb h^ct4 VX]^cZ»hhZii^c\h I t -h^c &*%% hdi]Vii]Zh^\cV %%%t'( #9ZhX a^hcdlYZÃcZYW g^WZi]ZVY_jhib n Zcihi]VilZgZb VYZ#
8]VeiZg* GZk^Zl
B=G '+.
3/5/08 4:27:57 PM
x MHR Functions and Applications 11 • A Tour of Your Textbook
FA 11 FM.indd 10
3/6/08 2:12:38 PM
Practice Test
8]VeiZg*EgV
Xi^XZIZhi
For questions
• Each chapter ends with a Practice Test. • All tests include some multiple choice questions. Practising this type of question will help you prepare for university or college entrance tests.
1 to 4, select
the best answ er. eZg^dYd[i]Z\gV e]h]dlc4
&# L]Vi^hi]Z y 2
+# 9ZiZgb ^cZi]
ZbZVhjgZd[Vc\a ZV^chiVcYVgY edh^i^dc!iddcZY ZX^bVaeaVXZ# h^ci]ZhZXdcYfj VYgVci #)**-!^[V^h^ci] Zi]^gY fjVYgVci
V h^cV%#* !^[V^
0
180°
–2
360°
x
Y h^cV%#% .+%!^
7 '
fjVYgVci
8 .%
6 i]Ze]VhZh]
^[i
d gZ[Zghid
7 i]ZVbea^ijY
Z
8 i]ZkZgi^XVa 9 i]ZeZg^dY
igVchaVi^dc
(#6cVc\aZV
^h^chiVcYVgYed h^i^dcl^i] iZgb^cVaVgb^c i]Zi]^gYfjVYgVc hiViZbZci^higjZ4 i#L]^X]
6 H^cV^hedh
^i^kZVcYXdhV^h cZ\Vi^kZ# Vi^kZVcYXdhV^ hcZ\Vi^kZ# ^i^kZVcYXdhV^h edh^i^kZ# #
7 H^cV^hcZ\ 8 H^cV^hedh
aZ^hcdiXdiZgb^c Val^i]&*%4
.#9ZiZgb^cZ
[jcXi^dc#
7 -,%
W +* Z '%% ] ',%
X]h^cZ
T!gZÄZXiZY^ci] ' Z
y=1
1
]Vc\aZ^chiVcYV gYed I]Zc!ÃcYil dXdiZgb^cVaVc\a h^i^dc# Zh[dgZVX] \^kZcVc\aZ#
0
X
180°
360°
540°
x
y 8
X &+% [ (%*
4
0 –4
180°
360°
540°
x
–8
s and Applications
&!]dg^odciVaVm
^hVadc\
&!]dg^odciVaVm ^hVadc\i]Z x"Vm^h!e]VhZh]^[ id[.%idi]Zg^\] i &!]dg^odciVaVm ^hVadc\i]Z x"Vm^h!e]VhZh]^[ id[(%idi]ZaZ[i &&# 6idnigVXid gl]ZZa]VhgVY^j hd[&Xb VcYgdiViZhXdjc iZgXadX`l^hZ#6h ZbWZYYZY^ci]Z idcZ^h l]ZZaVii]Zg^\] ed^ci!Vhh]dlc# ibdhi 9ZhXg^WZi]ZX]V h^cZ\gVe]^cZVX c\Zidi]Z &)# JhZIZX]cd ]h^ijVi^dc# ad\nI]ZcjbWZg d[eZdeaZ!^c b^aa^dch!l]djhZY ejWa^XigVch^i^c X^inYjg^c\Vcn\^ VaVg\Z kZcbdci]XVcWZ Wni]Z[jcXi^dcf x bdYZaaZY '#(h^c (%x l]ZgZxgZegZhZci (% )#,! hi]Zbdci]!l^i] ?VcjVgn&!;ZWg jVgn'!VcY hddc # V JhZV\gVe] stone ^c\XVaXjaVidgid \gVe]i]Z [jcXi^dc[dgdcZ nZVg# W 6eegdm^bV iZan]dlbVcne V I]Zl]ZZa^ ZdeaZjhZY ejWa^XigVch^i^c h'Xb^cgVY^jh# 6j\jhi4 W I]ZhidcZW X 9jg^c\l]^ Z\^ch^ci]Zjee X]bd Zgbdhi ci]lVhg^YZgh]^e edh^i^dc# ]^\]ZhiaZkZa4 Vi^ih X I]Zl]ZZag Y >cl]^X]il diViZhXadX`l^hZ# d Reasoning and &'# JhZIZX]cd bdci]hY^Y Proving ad\nI]ZY^hiVcX Representing Z!d!i]Vii]Z VWdji Communicating bddc^h[gdb:Vg i]!^c`^adbZigZh! Problem Solving )%%%%%% Zhi^bViZYjh^c\i XVcWZ Connecting ]Z[jcXi^dc eZdeaZjhZ Reflecting d t '**%%h^c &(#'&&t.% ( Selecting Tools and ejWa^XigVch^i4 l]ZgZt^hi]Zi^bZ Computational -&*%%! Strategies ^cYVnhV[iZgi]Z i]ZYVnl]Zci]Z eZg^\ZZ Z >cl]VilV nh bddc^hXadhZhiid :Vgi] # b^\]i\adWValVgb V JhZV\gVe] ^c\XVaXjaVidg\gV ^c\ V[[ZXi e]i] [jcXi^dc[dgild i]^hbdYZa4 Z XnXaZh# W ;^cYi]Zb Vm^bjbVcYb^c^ bjb Y^hiVcXZhi]Zbdd c^h[gdb:Vgi]# X =dlbVcn YVnh^hdcZXnXa Zd[i]Z bddc4
y 2
8 &'(%
ad\nI]Z]Z^\]i!h !^cbZigZh! d[Ved^cidcVWd Vi»hegdeZaaZg!gZaV hjg[VXZd[i]ZlViZ i^kZidi]Z g^hYZÃcZYWn h V %#&'h^c V.% %#)(!l i]ZgdiVi^dcVaVc\ ]ZgZV^h aZ!^cYZ\gZZh# V L^i]i]Z]Z aed[V\gVe]^c\X VaXjaVidg! h`ZiX]V\gVe]d[ i]Z[jcXi^dc [dgi]gZZ gdiVi^dchd[i]Ze gdeZaaZg# W L]Vildja YWZi]ZbVm^bj bVcY b^c^bjbYZei]h d[i]ZegdeZaaZg4 X 9ZiZgb^cZ i]ZYZei]d[i]Z\ ^kZced^ci dci]ZegdeZaaZgV [iZggdiVi^dchd[' VcY+%%#:meaV^c )% i]ZgZhjaih# 6X]^ZkZbZci8] ZX`
c\i]Z
X Vbea^ijYZ
VcZfjVi^dc[dgZV
x"Vm^h
9 ((%
FA 11 CH05.indd
y(
&(#JhZIZX]cd
*!]dg^odciVaVm ^hVad
Y Vbea^ijYZ
V Vbea^ijYZ & W
*# H`ZiX]ZVX
',%B=GFunction
W Vbea^ijYZ
iX]d[yh^cx[ dgdcZeZg^dY# ]Zed^cihl]ZgZy &VcY \^kZi]ZkVajZhd [x# W AdXViZVaai ]Zed^cihl]ZgZy %#,%,& VcY\^kZi]ZkVaj Zhd[x# X AdXViZVaai ]Zed^cihl]ZgZy %#* VcY\^kZi]ZkVaj Zhd[x# -# H`ZiX]V\g Ve]d[ZVX]h^cZ [jcXi^dc! h]dl^c\ildXnX aZh# V f x (h^c x W f x h^c x +% X f x h^cx *
9 IVcV^hcZ \Vi^kZ
Y &-%
x"Vm^h
[V^h^ci]ZhZXdc Y
V AdXViZVaai
[d^cyh^c x
)# L]^X]Vc\
V Vbea^ijYZ
,# 9gVlVh`Z
9 (+%
\ &.(
!^[V^h^ci]Z[djg i]
fjVYgVci
'# I]ZkVajZd
V (%
jVi^dc[dgZVX]h^c Z[jcX >cY^XViZi]Z^ciZ gkVah^cl]^X]i] i^dc# ^h^cXgZVh^c\VcY Z[jcXi^dc YZXgZVh^c\dkZg eZg^dY# dcZ
X iVcV' #'(+&
6 &-%
6 *&%
&%# Lg^iZVcZf
W XdhV% 540°
11 • 8]VeiZg*
270-271
8]VeiZg*EgVXi^XZ
IZhiB=G ',&
3/5/08 5:09:58 PM
Tasks • Tasks are presented at the end of each chapter. • These are more involved problems that require you to use several concepts from the chapter. Each task has multi-part questions. • Some tasks may be assigned as individual or group projects.
Earth facts:
12 P.M. 10 A.M.
8 A.M.
150 000 000 km
60°
Position of the sun relative to the horizon line
30° Horizon line 150 000 000 km
Earth’s rotation
6 A.M.
x y
Functions and Application
s 11 •
8]VeiZgh)VcY*GZk^Z
Chapter Review
l
8]VeiZg)Ig^\dcdbZign
)# L]ZcVXVi^h,b[
]Z^cY^XViZYh^YZ!idi]Z cZVgZhiiZci]d[Vjc^i#
• This feature appears at the end of each chapter. • By working through these questions, you will identify areas where you may need more review or study before doing the Practice Test.
V
W
C 55°
b
E
*# IldhXjWVY^kZghV
8.5 cm
gZ&%%bVeVgiVii]Z hVbZYZei]WZcZVi]i]ZlViZg »hhjg[VXZ# I]Z^gWdVi^hadXViZYWZilZZc i]Zild Y^kZghViVcVc\aZd[ZaZkVi^dc d[+%[gdb Y^kZg6VcY*)[gdb Y^kZg7#= ZVX]Y^kZg[gdbi]Z^gWdVi!id dl[Vg^h i]ZcZVgZhi bZigZ4
c
A
9.2 m
G
L
20°
f
64°
D
Y
2.1 cm
F
26°
C
B
X
1.8 m
K
k
+#I]Zedhihd[VhdXXZ
E
g\dVaVgZ,#(b VeVgi#BVgiV^h&'#*b[gdbd cZedhiVcY &(#'b[gdbi]Zdi]Zgedhi#L ^i]^cl]Vi Vc\aZ!idi]ZcZVgZhiYZ\gZZ!b jhih]Z`^X` i]ZhdXXZgWVaaidhXdgZV\dVa 4
J
'# ;^cYi]ZbZVhjgZd[
Wdi]VXjiZVc\aZh^c ZVX]ig^Vc\aZ!idi]ZcZVgZhiY Z\gZZ# V W E T
11 cm
7 cm
9m D
Cumulative Review
gdbV[ZcXZ!i]ZVc\aZ d[ZaZkVi^dcidi]Zided[i]Z[Z cXZ^h&+# L]Vi^hi]ZVc\aZd[ZaZkVi^dc l]Zci]ZXVi ^h(b[gdbi]Z[ZcXZ4GdjcY idi]ZcZVgZhi YZ\gZZ#
&# ;^cYi]ZaZc\i]d[i
F
R
13 m
8]VeiZg*/H^cZ;jcXi^dch ,# 9ZiZgb^cZl]Zi]Zg
dgcdiZVX]\gVe]^h eZg^dY^X#>[^i^h!YZiZgb^cZi] ZeZg^dY! Vbea^ijYZ!YdbV^c!VcYgVc\ Z#
S
V
(# HdakZZVX]ig^Vc\aZ
y
#GdjcYndjgVchlZghid i]ZcZVgZhiiZci]d[Vjc^i!^[c ZXZhhVgn#
V
W
A
4
N
9.1 cm
–4
0
4
8 x
–4
C
• A Cumulative Review occurs at the end of Chapters 3, 5, and 8. These questions allow you to review concepts you have learned in the chapters since the last Cumulative Review.
43°
12.7 cm
B
X
67°
L
23 cm Y 4.0 m 62 cm
H
58° 3.2 m
W y 4
Y
G
51° 2.3 m M
F
Z –4
0
4
8 x
–4
59 cm
',)B=GFunctions and Application
X
s 11 • 8]VeiZgh)VcY*GZk^
Zl
FA 11 CH05.indd 274
3/5/08 4:29:37 PM
A Tour of Your Textbook • MHR xi
FA 11 FM.indd 11
3/6/08 2:12:45 PM
Other Features The Mathematical Process These seven mathematical processes are integral to learning mathematics: • Problem Solving Reasoning and Proving • Reasoning and Proving Representing Communicating • Reflecting Problem Solving • Selecting Tools and Computational Strategies Connecting Reflecting • Connecting • Representing Selecting Tools and Computational Strategies • Communicating These processes are interconnected and are used throughout the course. Some examples and exercises are flagged with a mathematical processes graphic to show or remind you which of the processes are involved in solving the problem. ciZgZhi
I]Z[dgbjaV[dgXdbedjc Y^ciZgZhi^hA P &i n l]ZgZA^hi]ZVb ! djci!i]Z[jijgZkVajZd[V c^ckZhibZcidgad P^hi]Z dg^\^cVa eg^cX^eV Vc a^ckZhiZYdgWdggdlZY i^hi]Z^ciZgZhigViZeZgX dckZgh^dceZg^dY VhVYZ n^hi]Z cjbWZg d[XdckZ X^bVa gh^dceZg^dYh >[^ciZgZhi^hXdbedjcYZY dcXZeZgnZVg!i^hi]ZVcc >[^ciZgZhi^hXdbedjcYZY jVa^ciZgZhigViZ# 'i^bZheZgnZVg!i^hi]ZVc >[^ciZgZhi^hXdbedjcYZY cjVa^ciZgZhi'!n^hi]Z )i^bZheZgnZVg!i^hi]ZVc cjbWZgd[nZVgh'# >[^ciZgZhi^hXdbedjcYZY cjVa^ciZgZhi)!n^hi]Z bdci]an!i^hi]ZVccjVa cjbWZgd[nZVgh)# ^ciZgZhi &'!n ^hi]Zcj ;^cYi]ZVbdjci^[)%%% bWZgd[ nZVgh &'# lVhYZedh^iZYVi)#)eZ AP & i n gnZVg!XdbedjcYZYfjVg iZgan[dg +nZVgh# %#%)) + ) )%%% &TT ) )#%)) ') )%%% TT ) *'%&#%&
Round money amounts
I]ZgZ[dgZ!*'%&#%&ldja
to the nearest cent.
YWZi]ZVbdjciV[iZg+n
)'%B=GFunctions
ZVgh#
and Applications 11 • EgZgZfj^h^iZH`^aah6
eeZcY^m
FA 11 Prereq Skills Appendix.ind42
0 420
3/5/08 4:33:06 PM
IZX]cdad\n6eeZcY^m 8DCI:CIH The Geometer’s Sketchp ciZghZXi^d c 8dchigjXi^c\EVgVaaZaVcY EZgeZcY^XjaVgA^cZh Jh^c\i]ZBZVhjgZBZcj AVWZaVKZgiZm 8]Vc\^c\AVWZahd[BZVhjgZh Jh^c\i]ZDc"HXgZZc8VaXjaV idg Jh^c\IVWjaViZid8dchigjXiV 9ViVIVWaZ 8dchigjXi^c\VHa^YZg[dgV;j cXi^dc
I>"-(EajhVcYI>"-)Eaj h cidA^hih Jh^c\A^hiDeZgVi^dch
E6<: )(8aZVg^c\A^hih )(8VaXjaVi^c\;^ghiVcYHZXdcY )(9^[[ZgZcXZh )(. Ijgc^c\D[[6aaEadih 8]Vc\^c\i]Z6eeZVgVcXZd[ VA^cZ )(. Ijgc^c\D[[Vc:fjVi^dc )(. ;^cY^c\Vy">ciZgXZei )(. ;^cY^c\Vc>ciZghZXi^dcEd^ci ))% 8gZVi^c\VHXViiZgEadi ))% Ijgc^c\Dci]Z9^V\cdhi^X ))% Ijgc^c\D[[i]Z9^V\cdhi^X ))& ;^cY^c\V8jgkZdgA^cZd[7Z hi;^i ))' ;^cY^c\VOZgddgBVm^bjb$ ))' B^c^bjbKVajZ Jh^c\i]Z87G 8VaXjaVidg" 7VhZY ))' GVc\Zg ))' ))( I]ZIKBHdakZg ))) ))) 6Wdjii]Z;^cVcXZ6 eea^XVi^dch DeZc^c\i]ZIKBHdakZg ))) L]Vii]ZIKBHdakZgKVg^VWa Zh ))* GZegZhZci >ckZhibZcihVcYAdVch CdGZ\jaVgEVnbZcih E6<: )), )), )), )))))))))). )*% )*% )*&
)*& )*& )*' )*' )*' )*( )*( )*( )*) )*) )*) )** )*+
E6<: )*+ )*, )*, )*,
I>"-.I^iVc^jbc[dgbVi^dc ;gdbi]Z =dbZHXgZZcdgGZ"8dbeji^ c\ V8dbbVcY )*8aZVg^c\DjiDcZ"8] VgVXiZgKVg^VWaZh )*. 6XXZhh^c\V8ViVad\jZd[8db bVcYh )*. 8daaZXi^c\IZgbhL^i]DcZ KVg^VWaZ^c:VX]IZgb )*.
)(+B=GFunctions and Application
s 11 • IZX]cdad\n6eeZcY^m
FA 11 Tech Appendix.indd
436
Complete illustrated answers are provided for all questions in each Prerequisite Skills, numbered section, Chapter Review, Practice Test, and Cumulative Review. Refer to pages 482–555. Answers for Investigate, Communicate Your Understanding, and Achievement Check questions and Chapter Problem Wrap-Up are provided in Functions and Applications 11 Teacher’s Resource.
3/5/08 4:34:45 PM
Glossary
i^hVahd XVaaZYi]Z Vc\aZd[^cXa^cVi^dc#
]VibZVhjgZhaZhhi]Vc
.%#
angle of elevation
Vc\aZd[^cXa^cVi^dc6 cdi]ZgcVbZ[dgi]ZVc \aZd[ ZaZkVi^dc#
VXjiZig^Vc\aZ6ig^Vc \aZ^cl]^X]ZVX]d[i] Z^ciZg^dg Vc\aZhbZVhjgZhaZhhi ]Vc.%#
Vccj^in6hZg^Zhd[Zf jVaeVnbZcihdgYZedh ^ihZVgc^c\ XdbedjcY^ciZgZhiVcY bVYZVigZ\jaVg^ciZgk VahdkZgV ÃmZYeZg^dYd[i^bZ# 8VgeVnbZcih!bdgi\V\ ZeVnbZcih!VcYadVc eVnbZcihVgZVccj^i^Z h# VgZVI]ZcjbWZgd[hf jVgZjc^ihXdciV^cZY^c Vild" Y^bZch^dcVagZ\^dc#
Va\ZWgVi^aZh6XdaaZXi ^dcd[hfjVgZhVcYgZX iVc\aZh! l^i]Y^[[ZgZci"XdadjgZY h^YZh!jhZYidgZegZhZc ijc^ih VcYkVg^VWaZh# Va\ZWgV^XZmegZhh^dc 6bVi]ZbVi^XVae]gVh ZbVYZd[ cjbWZghVcYkVg^VWaZh !XdccZXiZYWndeZgVid ghhjX]Vh !!!VcY# *x'&^hVcVa\ZWgV^XZme gZhh^dc# Vbdgi^oVi^dcI]ZegdX Zhhd[\gVYjVaangZYjX^c \VYZWi i]gdj\]gZ\jaVgZfjVae VnbZcih#Bdgi\V\Zhd[i Zc]VkZ Vbdgi^oVi^dceZg^dYhd ['%dg'*nZVgh# VbdjciI]ZkVajZd[V c^ckZhibZcidgVadVc Vii]Z ZcYd[Vi^bZeZg^dY!XV aXjaViZYWnVYY^c\i]Z eg^cX^eVa VcY^ciZgZhi# Vbea^ijYZ=Va[i]ZY^ hiVcXZWZilZZci]ZbV m^bjb VcYb^c^bjbkVajZh d[VeZg^dY^X[jcXi^dc# >i^h XVaXjaViZYVh
TTT
TTT bVm^bjbk ^bjbkVaj VajZb^c Z T ' Vc\aZd[YZXa^cVi^dc6 cdi]ZgcVbZ[dgi]ZVc \aZd[ YZegZhh^dc#
Vc\aZd[YZegZhh^dcI ]ZVc\aZWZilZZci]Z] dg^odciVa VcYi]Za^cZd[h^\]iY dlcidVcdW_ZXi#>i^hV ahdXVaaZY i]ZVc\aZd[YZXa^cVi^d c# angle of depression
VhnbeidiZ6higV^\]i
a^cZi]ViVXjgkZVeegd
VX]Zh#
Vm^hd[hnbbZign d[V eVgVWdaV I]ZkZgi^XV aa^cZ i]ViY^k^YZhVeVgVWdaV ^cidildXdc\gjZci]Va kZhVcY ^ciZghZXihi]ZeVgVWdaV Vii]ZkZgiZm#
B WVhZ d[VedlZg I]Z cjbWZgjhZYVhV[VXi dg[dg gZeZViZYbjai^ea^XVi^d c# >c+(!i]ZWVhZ^h+# W^cVgncjbWZghnhiZb 6cjbWZghnhiZbi]V ijhZh ildhnbWdah!jhjVaan i]ZY^\^ih%VcY&!VcY deZgViZh^c WVhZ'idgZegZhZcicjb WZgkVajZh# &' & '( & '' % '& % '% &'!VcjbWZg^ci]ZYZ X^bVacjbWZghnhiZb! ^hgZegZhZciZYWn&&%% # W^cdb^Va6edancdb^V ai]Vi]VhildiZgbh# (x)^hVW^cdb^Va#
C X^gXaZI]ZhZid[Vaaed ^cih^ci]ZeaVcZi]ViVg Z Zfj^Y^hiVci[gdbVÃmZ Yed^ciXVaaZYi]ZXZci gZ# X^gXjb[ZgZcXZI]ZeZ g^bZiZgd[VX^gXaZ#
**+B=GFunctions and Application
s 11 •
