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{TEXT 257 25 "\nShifting and Stretching\n" }{TEXT 258 14 "(CCH Text 1.
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374 374 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 }}{PARA 13 "" 1 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 19 "The parameter k in " }
{XPPEDIT 18 0 "f(x+k) " "-%\"fG6#,&%\"xG\"\"\"%\"kGF'" }{TEXT -1 30 "s
hifts the graph to the left (" }{XPPEDIT 18 0 "k>0" "2\"\"!%\"kG" }
{TEXT -1 12 ") or right (" }{XPPEDIT 18 0 "k<0" "2%\"kG\"\"!" }{TEXT 
-1 2 ") " }{XPPEDIT 18 0 "k" "I\"kG6\"" }{TEXT -1 7 " units." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Problem
 3" }}{PARA 0 "" 0 "" {TEXT -1 8 "Clearly " }{XPPEDIT 18 0 "f(x+k)" "-
%\"fG6#,&%\"xG\"\"\"%\"kGF'" }{TEXT -1 17 " is not equal to " }
{XPPEDIT 18 0 "f(x)+k" ",&-%\"fG6#%\"xG\"\"\"%\"kGF'" }{TEXT -1 13 " e
xcept when " }{XPPEDIT 18 0 "k=0" "/%\"kG\"\"!" }{TEXT -1 51 ".  One s
hift is up and down the other is sideways.\n" }}}{SECT 1 {PARA 3 "" 0 
"" {TEXT -1 16 "Problems 4 and 5" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 
"S:= \{seq(f(x-k),k=0..4)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG
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gXwhIF_p7$Fix$\"1&oQ\">ZnsrF_p7$F^y$\"1%)QQ`OO+7F07$Fcy$\"1o5;0n`!*=F0
7$Fhy$\"1ZEkI#\\Bk#F07$F]z$\"1M\")R;;j&f$F07$Fbz$\"1(pZ2)prlYF07$Fgz$
\"\"'F*-F\\[l6&F^[lF_[lF*F_[l-%+AXESLABELSG6$%\"xG%\"yG-%%VIEWG6$;F(Fg
z;$!\"&F*$\"\"&F*" 2 374 374 374 2 0 1 0 2 9 0 4 2 1.000000 45.000000 
45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 
}}{PARA 0 "" 0 "" {TEXT -1 19 "The parameter k in " }{XPPEDIT 18 0 "f(
x+k) " "-%\"fG6#,&%\"xG\"\"\"%\"kGF'" }{TEXT -1 30 "shifts the graph t
o the left (" }{XPPEDIT 18 0 "k>0" "2\"\"!%\"kG" }{TEXT -1 12 ") or ri
ght (" }{XPPEDIT 18 0 "k<0" "2%\"kG\"\"!" }{TEXT -1 2 ") " }{XPPEDIT 
18 0 "k" "I\"kG6\"" }{TEXT -1 8 " units.\n" }}}{SECT 1 {PARA 3 "" 0 "
" {TEXT -1 9 "Problem 6" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "S:= \{se
q(k*f(x),k=0..4)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG<'\"\"!,&
*$%\"xG\"\"$F*F)!\"$,&F(\"\"#F)!\"#,&F(\"\"%F)!\"%,&F(\"\"\"F)!\"\"" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "plot(S,x=-3..3,y=-5..5);" }}{PARA 
13 "" 1 "" {INLPLOT "6)-%'CURVESG6$7S7$$!\"$\"\"!F*7$$!1+++vq@pG!#:F*7
$$!1++D^NUbFF.F*7$$!1++]K3XFEF.F*7$$!1++]F)H')\\#F.F*7$$!1++D'3@/P#F.F
*7$$!1++Dr^b^AF.F*7$$!1++D,kZG@F.F*7$$!1++Dh\")=,?F.F*7$$!1++DO\"3V(=F
.F*7$$!1+++NkzV<F.F*7$$!1++]d;%)G;F.F*7$$!1+++0)H%*\\\"F.F*7$$!1+++vl[
p8F.F*7$$!1+++&>iUC\"F.F*7$$!1++DhkaI6F.F*7$$!1+++]XF`**!#;F*7$$!1++++
Az2))FfnF*7$$!1++]7RKvuFfnF*7$$!1-+++P'eH'FfnF*7$$!1****\\7*3=+&FfnF*7
$$!1)***\\PFcpPFfnF*7$$!1)****\\7VQ[#FfnF*7$$!1)***\\i6:.8FfnF*7$$!1b+
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L&\\(>Ffn7$F[o$\"1@+#e&z2)H$Ffn7$F^o$\"1&*3_fbJ+QFfn7$Fao$\"1W6CP<X]PF
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$\"1I@h[)Rn&pFfn7$F_r$\"1\"f4iay2B\"F.7$Fbr$\"1mY[$o]#e=F.7$Fer$\"1.Py
`zLaEF.7$Fhr$\"1cX`3<h#e$F.7$F[s$\"1h_lu*[cs%F.7$F^s$\"1no$\\d/S+'F.7$
Fas$\"1Yc?'z2O](F.7$Fds$\"1v%**)R`#\\>*F.7$Fgs$\"19u&)=m'Q4\"Fhu7$Fjs$
\"1q\\fi9H<8Fhu7$F]t$\"12@c)3c&R:Fhu7$F`t$\"1Rnc![X5!=Fhu7$Fct$\"1=Yw6
$>h2#Fhu7$Fft$\"#CF*-Fit6&F[uF\\uF*F\\u-%+AXESLABELSG6$%\"xG%\"yG-%%VI
EWG6$;F(Fft;$!\"&F*$\"\"&F*" 2 374 374 374 2 0 1 0 2 9 0 4 2 1.000000 
45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 
0 0 0 0 1 }}{PARA 0 "" 0 "" {TEXT -1 14 "The parameter " }{XPPEDIT 18 
0 "k" "I\"kG6\"" }{TEXT -1 35 " stretches the graph away from the " }
{XPPEDIT 18 0 "x" "I\"xG6\"" }{TEXT -1 19 "-axis.  The larger " }
{XPPEDIT 18 0 "k" "I\"kG6\"" }{TEXT -1 33 " is, the larger the pull wi
ll be." }{MPLTEXT 1 0 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 9 "Problem 7" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 25 "S:= \{seq(f(k*x),k=0..4)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%\"SG<'\"\"!,&*$%\"xG\"\"$\"\")F)!\"#,&F(\"#FF)!\"$,&F(\"\"\"F)!\"\",&
F(\"#kF)!\"%" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "plot(S,x=-3..3,y=-5
..5);" }}{PARA 13 "" 1 "" {INLPLOT "6)-%'CURVESG6$7S7$$!\"$\"\"!F*7$$!
1+++vq@pG!#:F*7$$!1++D^NUbFF.F*7$$!1++]K3XFEF.F*7$$!1++]F)H')\\#F.F*7$
$!1++D'3@/P#F.F*7$$!1++Dr^b^AF.F*7$$!1++D,kZG@F.F*7$$!1++Dh\")=,?F.F*7
$$!1++DO\"3V(=F.F*7$$!1+++NkzV<F.F*7$$!1++]d;%)G;F.F*7$$!1+++0)H%*\\\"
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IEWG6$;F(Fft;$!\"&F*$\"\"&F*" 2 374 374 374 2 0 1 0 2 9 0 4 2 
1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 
0 0 180 0 0 0 0 0 0 1 }}{PARA 0 "" 0 "" {TEXT -1 14 "The parameter " }
{XPPEDIT 18 0 "k" "I\"kG6\"" }{TEXT -1 32 " stretches the graph toward
 the " }{XPPEDIT 18 0 "y" "I\"yG6\"" }{TEXT -1 19 "-axis.  The larger \+
" }{XPPEDIT 18 0 "k" "I\"kG6\"" }{TEXT -1 36 " is, the closer the grap
h is to the " }{XPPEDIT 18 0 "y" "I\"yG6\"" }{TEXT -1 6 "-axis." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "P
roblem 8" }}{PARA 0 "" 0 "" {XPPEDIT 18 0 "f(kx)" "-%\"fG6#%#kxG" }
{TEXT -1 17 " is not equal to " }{XPPEDIT 18 0 "kf(x)" "-%#kfG6#%\"xG
" }{TEXT -1 58 " since the stretching is with respect to different lin
es.\n" }}}}{MARK "8" 0 }{VIEWOPTS 1 1 0 1 1 1803 }