Expression 39: "f" Subscript, "x" , Baseline left parenthesis, "x" , "L" Subscript, "d" , Baseline , right parenthesis equals "L" Subscript, "d" , Baseline left bracket, 1 , right bracket . "x" plus Start sum from "n" equals 1 to length left parenthesis, "L" Subscript, "d" , Baseline , right parenthesis minus 1, end sum, "f" Subscript, 01 "a" , Baseline left parenthesis, "x" minus "n" , "a" , right parenthesis left parenthesis, "L" Subscript, "d" , Baseline left bracket, "n" plus 1 , right bracket . "x" minus "L" Subscript, "d" , Baseline left bracket, "n" , right bracket . "x" , right parenthesisfxx,Ld=Ld1.x+lengthLd−1∑n=1f01ax−n,aLdn+1.x−Ldn.x
39
Expression 40: "f" Subscript, "y" , Baseline left parenthesis, "x" , "L" Subscript, "d" , Baseline , right parenthesis equals "L" Subscript, "d" , Baseline left bracket, 1 , right bracket . "y" plus Start sum from "n" equals 1 to length left parenthesis, "L" Subscript, "d" , Baseline , right parenthesis minus 1, end sum, "f" Subscript, 01 "a" , Baseline left parenthesis, "x" minus "n" , "a" , right parenthesis left parenthesis, "L" Subscript, "d" , Baseline left bracket, "n" plus 1 , right bracket . "y" minus "L" Subscript, "d" , Baseline left bracket, "n" , right bracket . "y" , right parenthesisfyx,Ld=Ld1.y+lengthLd−1∑n=1f01ax−n,aLdn+1.y−Ldn.y
40
Expression 41: "f" Subscript, 40 , Baseline left parenthesis, "t" , "L" Subscript, "d" , Baseline , right parenthesis equals left parenthesis, "f" Subscript, "x" , Baseline left parenthesis, "t" , "L" Subscript, "d" , Baseline , right parenthesis , "f" Subscript, "y" , Baseline left parenthesis, "t" , "L" Subscript, "d" , Baseline , right parenthesis , right parenthesisf40t,Ld=fxt,Ld,fyt,Ld
41
Expression 42: "f" Subscript, 4 , Baseline left parenthesis, "t" , "L" Subscript, 0 , Baseline , right parenthesis equals "f" Subscript, 40 , Baseline left parenthesis, "t" , "L" Subscript, 0 , Baseline left bracket, floor left parenthesis, StartFraction, left bracket, 1 , ... , 2length left parenthesis, "L" Subscript, 0 , Baseline , right parenthesis , right bracket plus 1 Over 2 , EndFraction , right parenthesis , right bracket , right parenthesisf4t,L0=f40t,L0floor1,...,2lengthL0+12
42
Expression 43: "f" Subscript, 4 , Baseline left parenthesis, "t" , "L" , right parenthesisf4t,L
domain t Minimum: 0.50.5
less than or equal to "t" less than or equal to≤t≤
domain t Maximum: 2length left parenthesis, "L" , right parenthesis plus 0.52lengthL+0.5
43
Hidden Label: "L" Subscript, 2 , Baseline equals "L" left bracket, floor left parenthesis, StartFraction, left bracket, 1 , ... , 2length left parenthesis, "L" , right parenthesis , right bracket plus 1 Over 2 , EndFraction , right parenthesis , right bracketL2=Lfloor1,...,2lengthL+12
Label
equals=
left parenthesis, 1.5 5 5 , 1.0 5 , right parenthesis1.555,1.05
left parenthesis, 1.5 5 5 , 1.0 5 , right parenthesis1.555,1.05
left parenthesis, 1.0 7 , 1.4 8 , right parenthesis1.07,1.48
left parenthesis, 1.0 7 , 1.4 8 , right parenthesis1.07,1.48
left parenthesis, 0.9 3 , 0.9 2 6 , right parenthesis0.93,0.926
left parenthesis, 0.9 3 , 0.9 2 6 , right parenthesis0.93,0.926
left parenthesis, 0.4 4 , 0.6 6 5 , right parenthesis0.44,0.665
left parenthesis, 0.4 4 , 0.6 6 5 , right parenthesis0.44,0.665
left parenthesis, 0.3 0 5 , 0.2 3 6 , right parenthesis0.305,0.236
left parenthesis, 0.3 0 5 , 0.2 3 6 , right parenthesis0.305,0.236
left parenthesis, negative 0.9 8 5 , 1.5 6 4 , right parenthesis−0.985,1.564
left parenthesis, negative 0.9 8 5 , 1.5 6 4 , right parenthesis−0.985,1.564
44
Application: Transform functions
Hide this folder from students.
45
Expression 46: "g" Subscript, 0 , Baseline left parenthesis, "t" , "x" , right parenthesis equals "f" Subscript, 2 , Baseline left parenthesis, "x" , left bracket, "g" Subscript, 1 , Baseline left parenthesis, "t" , right parenthesis , "g" Subscript, 2 , Baseline left parenthesis, "t" , right parenthesis , right bracket , right parenthesisg0t,x=f2x,g1t,g2t
46
Expression 47: "g" Subscript, 1 , Baseline left parenthesis, "t" , right parenthesis equals left parenthesis, sin 2 "t" , sin 3 "t" , right parenthesisg1t=sin2t,sin3t
47
Expression 48: "g" Subscript, 2 , Baseline left parenthesis, "t" , right parenthesis equals left parenthesis, sin 7 "t" , sin 4 "t" , right parenthesisg2t=sin7t,sin4t
48
Expression 49: "g" Subscript, 3 , Baseline left parenthesis, "t" , right parenthesis equals left parenthesis, sin 4 "t" , sin 5 "t" , right parenthesisg3t=sin4t,sin5t
49
Expression 50: "g" Subscript, 4 , Baseline left parenthesis, "t" , right parenthesis equals left parenthesis, sin 2 "t" , sin 7 "t" , right parenthesisg4t=sin2t,sin7t
50
Expression 51: "g" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis equals left parenthesis, sin 6 "t" , sin 7 "t" , right parenthesisg5t=sin6t,sin7t
51
Expression 52: "g" left parenthesis, "t" , right parenthesis equals left bracket, "g" Subscript, 1 , Baseline left parenthesis, "t" , right parenthesis , "g" Subscript, 2 , Baseline left parenthesis, "t" , right parenthesis , "g" Subscript, 3 , Baseline left parenthesis, "t" , right parenthesis , "g" Subscript, 4 , Baseline left parenthesis, "t" , right parenthesis , "g" Subscript, 5 , Baseline left parenthesis, "t" , right parenthesis , right bracketgt=g1t,g2t,g3t,g4t,g5t
52
Expression 53: 1 quarter times "g" left parenthesis, "t" , right parenthesis plus left parenthesis, 1.1 times left bracket, negative 1 , 2 quarters minus 1 , ... , 1 , right bracket , negative 1.4 , right parenthesis14·gt+1.1·−1,24−1,...,1,−1.4
00
domain t Minimum:
less than or equal to "t" less than or equal to≤t≤
domain t Maximum: 2 pi2π
53
Expression 54: "g" Subscript, "m" "o" "d" , Baseline left parenthesis, "t" , right parenthesis equals join left parenthesis, "g" left parenthesis, "t" , right parenthesis left bracket, floor left parenthesis, StartFraction, left bracket, 1 , ... , 2length left parenthesis, "g" left parenthesis, 0 , right parenthesis , right parenthesis , right bracket plus 1 Over 2 , EndFraction , right parenthesis , right bracket , "g" left parenthesis, "t" , right parenthesis left bracket, 1 , right bracket , right parenthesisgmodt=joingtfloor1,...,2lengthg0+12,gt1
54
Expression 55: "f" Subscript, 40 , Baseline left parenthesis, "T" , "g" Subscript, "m" "o" "d" , Baseline left parenthesis, "t" , right parenthesis , right parenthesisf40T,gmodt
00
domain t Minimum:
less than or equal to "t" less than or equal to≤t≤
domain t Maximum: 2 pi2π
55
Expression 56: "g" left parenthesis, "t" , right parenthesisgt
00
domain t Minimum:
less than or equal to "t" less than or equal to≤t≤
