{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 } {PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 33 "Horizontal and Vertical S hiftings" }}{PARA 19 "" 0 "" {TEXT -1 16 "Dr. Wei-Chi Yang" }}{PARA 0 "" 0 "" {TEXT 256 10 "Objective:" }}{PARA 0 "" 0 "" {TEXT -1 115 "By t he end of this exercise, you would need to know when a function will b e shifted to the left, right, up or down." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "plot(3*x-2, x=-5..5, y=-10..10);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 24 "plot(-2*x^2+1, x=-5..5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(abs(x), x=-5..5);" }}}{EXCHG {PARA 0 " " 0 "" {TEXT 257 4 "Note" }{TEXT -1 40 ": You should remember the grap h of y = " }{XPPEDIT 18 0 "abs(x);" "6#-%$absG6#%\"xG" }{TEXT -1 2 ". " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "plot(\{abs(x), abs(x+1 ), abs(x)-2\}, " }{TEXT -1 0 "" }{MPLTEXT 1 0 29 "x=-5..5,y=-2..2,thic kness=3);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 258 4 "Note " }{TEXT -1 55 ". For the graphs above, do you know which one is which ?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "with(plots): implicitp lot(x^2+y^2 =1, x =-2..2, y=-2..2,\n scaling=constrained); " }}} {EXCHG {PARA 0 "" 0 "" {TEXT 259 8 "Exercise" }{TEXT -1 94 ": Can you \+ modify the equation above to get a plot of a circle, centered at (-2, \+ 4) and radius " }{XPPEDIT 18 0 "sqrt(5);" "6#-%%sqrtG6#\"\"&" }{TEXT -1 2 "? " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "animate(x^2+a, x=-5..5, a=-3..3, color=red);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 4 "Note" } {TEXT -1 83 ". Do you see that the animation above is going from botto m to top? Do you know why?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "animate((x^3+a), x=-5..5, a=-30..30, color=black, thi ckness=3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "animate((x+a) ^2, x=-20..20, a=-3..3, color=black);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 261 11 "Note. [1] " }{TEXT -1 71 "Do you see tha t the parabola is moving from the right to the left? Why?" }}{PARA 0 " " 0 "" {TEXT -1 43 "[2] You need to remember the graph of y = " } {XPPEDIT 18 0 "x^2;" "6#*$%\"xG\"\"#" }{TEXT -1 1 "." }}}{EXCHG {PARA 3 "" 0 "" {TEXT -1 26 "Compressions and Streching" }}{PARA 0 "" 0 "" {TEXT -1 69 "Notice that y=af(x) is a compression (vertical direction) of y=f(x) . " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "plot(\{sqrt(x-2),2*sqrt(x-2),(1/2)*sqrt(x-2)\},x =0..4,y=0..4,thickness=3); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "Ex ercise: Do you know which one is which for the graph above?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f :=x->(x+2)^3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "g:=x->2*(x +2)^3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "h:=x->(1/2)*(x+2) ^3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "plot(\{f,g,h\},-4..2 ,-8..8, thickness=3);\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "Do you know which one is which? Compare f(0), g(0) and h(0)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f(0); g(0); h(0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f:=x->-(x-2)^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "g:=x->-2*(x-2)^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "h:=x->(-1/2)*(x-2)^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "plot(\{f,g,h\},0..4,-10..4, thickness=3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f(3);g(3);h(3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Exercise: Do you which one is which?" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 66 "Note that y=f(ax) \+ is a streching (horizontal direction) of y=f(x)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f:=x->sin(x );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "g:=x->f(2*x);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "g(x);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 21 "plot(f(x),x=0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "plot(g(x),x=0..2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "plot(\{f(x),g(x)\},x=0..2*Pi,thickness=2);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 1 0" 16 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }