~v358 200 ~w207 205 453 766 0 6619 0 0 ~f? 14 12 10 ? 3 1 1 1 ? ? ? "Times" ? ? ? 1 ? 0 1 "Times" 12 ? ? 5 0 c n 100 1 0 0 k 576 m"?n \kj1994, Robert R. Curtis & Phil R. Smith. The Finley Pr\ ess." ? 0 26177 26178 26115 26178 1 1 1 1 0 0 8405120 0 -1 0 0 -1 -1 -1 -1 -1 1 1 1 0 2 0 0 0 0 0 0 ? ? ? ? ? ? ? ? ~Q ]|Expr|[#b @`bb#_b#_b#_}))# b(6" *~: ;8&c54 LiveMath Fundamentals| |,Z `f"}Advanced Graphing}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p3 0 ~V?v0 (k)~p0 1 ~V?f0 (omicron)~p0 1 ~V?f0 (lambda)~p0 1 ~V?f0 (phi)~p0 1 ~V?f0 (tau)~p0 1 ~V?f0 (epsilon)~p0 1 ~V?f0 (mu)~p0 1 ~V?f0 (rho)~p0 1 ~V?f0 (delta)~p0 1 ~V?f0 (xi)~p0 1 ~V?f0 (gamma)~p0 1 ~V?f0 (theta)~p0 1 ~V?f0 (zeta)~p0 1 ~V?f0 (psi)~p0 1 ~V?f0 (beta)~p0 1 ~V?f0 (pi)~p0 1 ~V?f0 (alpha)~p0 1 ~V?f0 (omega)~p0 1 ~V?v0 (diffQ)~p0 1 ~V?f0 (DiffQuotient)~p0 1 ~V?f0 (g)~p0 1 ~V?f0 (Diff)~p0 1 ~V?v0 (diffQuotient)~p0 1 ~V?f274 (arctan)~p0 1 ~V?f307 (ln)~p0 1 ~V?c2 (e)~p0 1 ~V?v0 (h)~p0 1 ~V?f258 (tan)~p0 1 ~V?v0 (mSec)~p0 1 ~V?v0 (b)~p0 1 ~V?v0 (sec)~p0 1 ~V?v0 (m)~p0 1 ~V?f0 (f)~p0 1 ~V?v0 (y')~p0 1 ~V?c4 (i)~p0 1 ~V?f32 (log)~p0 1 ~V?f257 (cos)~p0 1 ~V?f256 (sin)~p0 1 ~V?c1 ('p)~p0 1 ~V?c0 (n)~p0 1 ~V?c0 (c)~p0 1 ~V?v0 (a)~p0 1 ~V?v0 (z)~p0 1 ~V?v0 (y)~p0 1 ~V?v0 (x)~p1 1 ~A(alpha(?x)=sin(5*?x))~p0 2 ~d~A(beta(?x)=cos(?x-1))~p0 2 ~d~A(gamma(?x)=sin(?x)-1)~p0 2 ~d~A(delta(?x)=5*cos(?x))~p0 2 ~A(epsilon(?x)=0.5*sin(?x+2))~p0 2 ~A(zeta(?x)=2*cos(2*?x)-2)~p0 2 ~d~A(lambda(?x)=2*cos(1/2*x)+1/2)~p0 2 ~d~A(tau(?x)=-sin(?x+2))~p0 2 ~A(omega(?x)=2*cos(3*?x))~p0 2 ~d~A(theta(?x)=2^?x+5)~p0 2 ~d~A(rho(?x)=5^?x)~p0 2 ~d~A(omicron(?x)=5*?x+1)~p0 2 ~A(pi(?x)=4*ln(?x))~p0 2 ~d~A(psi(?x)=ln(?x-4))~p0 2 ~d~A(xi(?x)=2^(?x-2))~p0 2 ~d~A(mu(?x)=-(?x-3)^4)~p0 2 ~A(phi(?x)=-?x^3+3)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b(,[#! ))# b(,`fb"@}" *~: ;8&c54 Notebook| | and Quiz,Z C9}& b!( b"0 b#8 b$@ b%H b&P!WW}`f }) # b(,| |}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b(,}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})7# b) " *~: ;bP8&c55*If you are the | |Business Calculus student,L skip this notebook entirely,N| |}& b!( b"0 b#8 b$@ b%H b&P WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b(,["! )$# b(,`fb!M}" *~: ;b D&c54!PART| | I,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })b L# b(,`fb!M};2&c54 First| | we shall review some precalculus facts about scaling,L shifting| |,L reflecting,L and stretching of functions,L in a series of | |investigations,N}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%L[%! )$# b%L`f"}" *~: ;b D&c54 Investigation| | I,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })5# b%L`f"}y ,] f,Hx,I | |versus y ,] /0 f,Hx,I}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })6# b%L| |;.a,N Graph the top function of each pair given below,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW})6# b%Lb,N Then use the "!Times~:!;,Add| | Line Plot: ;. command to graph }& b!( b"0 b#8 b$@ b%H b&P!WW}| |)7# b%L the second function on the same set of axes,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~T~A(y=sin(x))~p0 0 ~A(y_1=-sin(x))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})2# b%,`f"}" *~: ;.&c54!Compare&c54 | |the graphs of the two functions above,N | |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=ln(x))~p0 0 ~A(y_1=-ln(x))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})0# b%,`f"}" *~: ;.&c54!Compare&c54 | |the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=2^x)~p0 0 ~A(y_1=-2^x)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})0# b%,`f"}" *~: ;.&c54!Compare&c54 | |the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$," *~: ;2&c54 General Observation| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~T~A(y=f(x))~p0 0 ~A(y_1=-f(x))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[$! )5# b%,`f"}" *~: ;.&c54!Suppose| |&c54 that y ,] f,Hx,I is any function whatsoever,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })b F# b%,`f"}&c54!Describe&c54 | |the effect that ,Ba minus sign in front of the function,B will| | have on the second graph,N}& b!( b"0 b#8 b$@ b%H b&P!WW}`f }) # b%,| |}& b!( b"0 b#8 b$@ b%H b&P!WW})(# b%,`f"}"!Times~:!;,Write | |your description below,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}) # b$,}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%L[%! )$# b%L`f"}" *~: ;b D&c54 Investigation| | II,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })4# b%L`f"}y ,] f,Hx,I| | versus y ,] f,H/0x,I}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })6# b%L| |;.a,N Graph the top function of each pair given below,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW})6# b%Lb,N Then use the "!Times~:!;,Add| | Line Plot: ;. command to graph }& b!( b"0 b#8 b$@ b%H b&P!WW}| |)7# b%L the second function on the same set of axes,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~T~A(y=sin(x))~p0 0 ~A(y_1=sin(-x))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})0# b%,`f"}" *~: ;.&c54!Compare&c54 | |the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=ln(x))~p0 0 ~A(y_1=ln(-x))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})0# b%,`f"}" *~: ;.&c54!Compare&c54 | |the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=2^x)~p0 0 ~A(y_1=2^(-x))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})0# b%,`f"}" *~: ;.&c54!Compare&c54 | |the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=f(x))~p0 0 ~A(y_1=f(-x))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[$! )5# b%,`f"}" *~: ;.&c54!Suppose| |&c54 that y ,] f,Hx,I is any function whatsoever,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })b H# b%,`f"}&c54!Describe&c54 | |the effect that ,Ba minus sign in front of the variable x,B will| | have on the second graph,N}& b!( b"0 b#8 b$@ b%H b&P!WW}`f }) # b%,| |}& b!( b"0 b#8 b$@ b%H b&P!WW})(# b%,`f"}"!Times~:!;,Write | |your description below,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}) # b$,}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%L[%! )$# b%L`f"}" *~: ;b D&c54 Investigation| | III,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })5# b%L`f"}y ,] f,Hx,I| | versus y ,] &c54$k&c54 f,Hx,I}& b!( b"0 b#8 b$@ b%H b&P!WW}| |`f })6# b%L;.a,N Graph the top function of each pair given below| |,N}& b!( b"0 b#8 b$@ b%H b&P!WW})6# b%Lb,N Then use the "!Times~:!;,Add| | Line Plot: ;. command to graph }& b!( b"0 b#8 b$@ b%H b&P!WW}| |)7# b%L the second function on the same set of axes,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~T~A(y=cos(x))~p0 0 ~A(y_1=2*cos(x))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })2# b%,`f"}&c54!What&c54 &c54!effect| |&c54 does ,B2 multiplied by the function,B | |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })*# b%,`f"}have on the second| | graph,_}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=cos(x))~p0 0 ~A(y_1=3*cos(x))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })2# b%,`f"}&c54!What&c54 &c54!effect| |&c54 does ,B3 multiplied by the function,B | |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })*# b%,`f"}have on the second| | graph,_}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=cos(x))~p0 0 ~A(y_1=1/3*cos(x))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })4# b%,`f"}&c54!What&c54 &c54!effect| |&c54 does ,B1,O3 multiplied by the function,B | |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })*# b%,`f"}have on the second| | graph,_}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=2^x)~p0 0 ~A(y_1=2*2^x)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })2# b%,`f"}&c54!What&c54 &c54!effect| |&c54 does ,B2 multiplied by the function,B | |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })*# b%,`f"}have on the second| | graph,_}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=2^x)~p0 0 ~A(y_1=3*2^x)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })2# b%,`f"}&c54!What&c54 &c54!effect| |&c54 does ,B3 multiplied by the function,B | |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })*# b%,`f"}have on the second| | graph,_}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=2^x)~p0 0 ~A(y_1=1/3*2^x)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })4# b%,`f"}&c54!What&c54 &c54!effect| |&c54 does ,B1,O3 multiplied by the function,B | |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })*# b%,`f"}have on the second| | graph,_}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=f(x))~p0 0 ~A(y_1=k*f(x))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[$! )5# b%,`f"}" *~: ;.&c54!Suppose| |&c54 that y ,] f,Hx,I is any function whatsoever,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })b F# b%,`f"}&c54!Describe&c54 | |the effect that ,Bthe constant ;8&c54$k;. &c54 multiplied by| | the function,B will have on the second graph,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f }) # b%,| |}& b!( b"0 b#8 b$@ b%H b&P!WW})(# b%,`f"}"!Times~:!;,Write | |your description below,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}) # b%4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b&,[&! )$# b&,`f"}" *~: ;b D&c54 Investigation| | IV,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })5# b&,`f"}y ,] f,Hx,I| | versus y ,] f,H&c54$k&c54 x,I}& b!( b"0 b#8 b$@ b%H b&P!WW}| |`f })(# b&,`f"}-;Trigonometric functions only,N-=| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })6# b&,;.a,N Graph the top| | function of each pair given below,N}& b!( b"0 b#8 b$@ b%H b&P!WW}| |)6# b&,b,N Then use the "!Times~:!;,Add Line Plot: ;. command| | to graph }& b!( b"0 b#8 b$@ b%H b&P!WW})7# b&, the second| | function on the same set of axes,N}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~T~A(y=sin(x))~p0 0 ~A(y_1=sin(2*x))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })1# b%,`f"}&c54!What&c54 &c54!effect| |&c54 does ,Ba 2 multiplied by the }& b!( b"0 b#8 b$@ b%H b&P!WW}| |`f })/# b%,`f"}variable x,B have on the second graph,_| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=sin(x))~p0 0 ~A(y_1=sin(3*x))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })1# b%,`f"}&c54!What&c54 &c54!effect| |&c54 does ,Ba 3 multiplied by the }& b!( b"0 b#8 b$@ b%H b&P!WW}| |`f })/# b%,`f"}variable x,B have on the second graph,_| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=sin(x))~p0 0 ~A(y_1=sin(1/3*x))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })3# b%,`f"}&c54!What&c54 &c54!effect| |&c54 does ,Ba 1,O3 multiplied by the | |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })/# b%,`f"}variable x,B have| | on the second graph,_}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=f(x))~p0 0 ~A(y_1=f(k*x))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%L[$! )7# b%L`f"}" *~: ;.&c54!Suppose| |&c54 that y ,] f,Hx,I is any trigonometric function whatsoever| |,N}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })b I# b%L`f"}&c54!Describe| |&c54 the effect that ,Bthe constant ;8&c54$k;.&c54 multiplied| | by the variable x,B will have on the second trigonometric graph| |,N}& b!( b"0 b#8 b$@ b%H b&P!WW}`f }) # b%L| |}& b!( b"0 b#8 b$@ b%H b&P!WW})(# b%L`f"}"!Times~:!;,Write | |your description below,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}) # b$,}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b&,[%! )$# b&,`f"}" *~: ;b D&c54 Investigation| | V,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })7# b&,`f"}y ,] f,Hx,I | |versus y ,] f,H&c54$x /0 h&c54 ,I}& b!( b"0 b#8 b$@ b%H b&P!WW}| |`f })6# b&,;.a,N Graph the top function of each pair given below| |,N}& b!( b"0 b#8 b$@ b%H b&P!WW})6# b&,b,N Then use the "!Times~:!;,Add| | Line Plot: ;. command to graph }& b!( b"0 b#8 b$@ b%H b&P!WW}| |)7# b&, the second function on the same set of axes,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~T~A(y=cos(x))~p0 0 ~A(y_1=cos(x-2))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })0# b%,`f"}&c54!What&c54 &c54!effect| |&c54 does ,B/02 added to the }& b!( b"0 b#8 b$@ b%H b&P!WW}`f })/# b%,| |`f"}variable x,B have on the second graph,_| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=cos(x))~p0 0 ~A(y_1=cos(x-4))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })0# b%,`f"}&c54!What&c54 &c54!effect| |&c54 does ,B/04 added to the }& b!( b"0 b#8 b$@ b%H b&P!WW}`f })/# b%,| |`f"}variable x,B have on the second graph,_| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=cos(x))~p0 0 ~A(y_1=cos(x+2))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })0# b%,`f"}&c54!What&c54 &c54!effect| |&c54 does ,B,K2 added to the }& b!( b"0 b#8 b$@ b%H b&P!WW}`f })/# b%,| |`f"}variable x,B have on the second graph,_| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=x^2)~p0 0 ~A(y_1=(x-2)^2)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })0# b%,`f"}&c54!What&c54 &c54!effect| |&c54 does ,B/02 added to the }& b!( b"0 b#8 b$@ b%H b&P!WW}`f })/# b%,| |`f"}variable x,B have on the second graph,_| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=x^2)~p0 0 ~A(y_1=(x-4)^2)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })0# b%,`f"}&c54!What&c54 &c54!effect| |&c54 does ,B/04 added to the }& b!( b"0 b#8 b$@ b%H b&P!WW}`f })/# b%,| |`f"}variable x,B have on the second graph,_| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=x^2)~p0 0 ~A(y_1=(x+2)^2)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })0# b%,`f"}&c54!What&c54 &c54!effect| |&c54 does ,B,K2 added to the }& b!( b"0 b#8 b$@ b%H b&P!WW}`f })/# b%,| |`f"}variable x,B have on the second graph,_| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=f(x))~p0 0 ~A(y_1=f(x-h))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%L[%! )7# b%L`f"}" *~: ;.&c54!Suppose| |&c54 that y ,] f,Hx,I is any trigonometric function whatsoever| |,N}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })6# b%L`f"}&c54!Describe&c54 | |the effect that ,Bthe constant ;8&c54$h;.&c54 subtracted to| | the }& b!( b"0 b#8 b$@ b%H b&P!WW}`f })1# b%L`f"}variable x,B| | will have on the second graph,N}& b!( b"0 b#8 b$@ b%H b&P!WW}| |`f }) # b%L}& b!( b"0 b#8 b$@ b%H b&P!WW})(# b%L`f"}"!Times~:!;,Write| | your description below,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}) # b$,}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b&,[%! )$# b&,`f"}" *~: ;b D&c54 Investigation| | VI,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })7# b&,`f"}y ,] f,Hx,I| | versus y ,] f,H&c54$x&c54 ,I ,K k}& b!( b"0 b#8 b$@ b%H b&P!WW}| |`f })6# b&,;.a,N Graph the top function of each pair given below| |,N}& b!( b"0 b#8 b$@ b%H b&P!WW})6# b&,b,N Then use the "!Times~:!;,Add| | Line Plot: ;. command to graph }& b!( b"0 b#8 b$@ b%H b&P!WW}| |)7# b&, the second function on the same set of axes,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~T~A(y=sin(x))~p0 0 ~A(y_1=sin(x)+1)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })2# b%,`f"}&c54!What effect| |&c54 does the ,B,K1 added to the }& b!( b"0 b#8 b$@ b%H b&P!WW}| |`f })-# b%,`f"}function,B have on the second graph,_| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=sin(x))~p0 0 ~A(y_1=sin(x)+4)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })2# b%,`f"}&c54!What effect| |&c54 does the ,B,K4 added to the }& b!( b"0 b#8 b$@ b%H b&P!WW}| |`f })-# b%,`f"}function,B have on the second graph,_| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=sin(x))~p0 0 ~A(y_1=sin(x)-2)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })2# b%,`f"}&c54!What effect| |&c54 does the ,B/02 added to the }& b!( b"0 b#8 b$@ b%H b&P!WW}| |`f })-# b%,`f"}function,B have on the second graph,_| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=e^x)~p0 0 ~A(y_1=e^x+1)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })2# b%,`f"}&c54!What effect| |&c54 does the ,B,K1 added to the }& b!( b"0 b#8 b$@ b%H b&P!WW}| |`f })-# b%,`f"}function,B have on the second graph,_| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=e^x)~p0 0 ~A(y_1=e^x+4)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })2# b%,`f"}&c54!What effect| |&c54 does the ,B,K4 added to the }& b!( b"0 b#8 b$@ b%H b&P!WW}| |`f })-# b%,`f"}function,B have on the second graph,_| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=e^x)~p0 0 ~A(y_1=e^x-2)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%,[#! )0# b%,`f"}" *~: ;.&c54!Compare| |&c54 the graphs of the two functions above,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })2# b%,`f"}&c54!What effect| |&c54 does the ,B/02 added to the }& b!( b"0 b#8 b$@ b%H b&P!WW}| |`f })-# b%,`f"}function,B have on the second graph,_| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=f(x))~p0 0 ~A(y_1=f(x)+k)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b%L[%! )7# b%L`f"}" *~: ;.&c54!Suppose| |&c54 that y ,] f,Hx,I is any trigonometric function whatsoever| |,N}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })6# b%L`f"}&c54!Describe&c54 | |the effect that ,Bthe constant ;8&c54$k;.&c54 added to the | |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })/# b%L`f"}function,B will | |have on the second graph,N}& b!( b"0 b#8 b$@ b%H b&P!WW}`f }) # b%L| |}& b!( b"0 b#8 b$@ b%H b&P!WW})(# b%L`f"}"!Times~:!;,Write | |your description below,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}) # b$,}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b(,[)! )$# b(,`f"}" *~: ;b D&c54!PART| | II,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })b M# b(,`fb!M};2&c54 Next| |,L we shall practice guessing the algebraic description of a| | function from just knowing its graph,N Here are some mystery| | functions}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })*# b(,`fb!M}for | |you to practice on,N}& b!( b"0 b#8 b$@ b%H b&P!WW}`f }) # b(,| |}& b!( b"0 b#8 b$@ b%H b&P!WW})b X# b(,`f"};.&c54!The mystery| | functions in the first part of this notebook are made up of | |simple transformations of the basic functions that we studied| | Part I of this notebook,N}& b!( b"0 b#8 b$@ b%H b&P!WW}`f }) # b(,| |}& b!( b"0 b#8 b$@ b%H b&P!WW})b E# b(,`f"};8&c54 Here is an | |example of how to determine the algebraic description a mystery| | function named ,Bomega,Hx,I,B,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}| |`f }) # b(,}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b(,| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~T~Q ]|Expr|[#b @`bb#_b#_b#_})'# b!," *~: ;.&c54 Example ,HFirst try| |,I}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~A(y=omega(x))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b#D`fb#_}" *~: ;bP8&c55*`g| |pc%^Jc$R&| |9SNNI!!!"q!87Db!riZ/s8M&O!([(i!([(i!!!!!!2T\L!(EM!1E0Q!s&B$bg-7f!7(TGbl7[Grr=k@| |rrW9$s-_14rW(7D!h'&gY5\Kili.%es8U(H[O!87AP| |RI'qV!<3$!bg6:l!<8Je!71ZJbQ.YC!3lJ'1[P,E!<3$!REtm9!<4kT!71ZJ| |R/m6e!3lJ'RI'qV!<3$!bg6:l!<8Je!71ZJbQ.YC!8.;O>(H[O!87APRI'qR| |!<2uu!71ZJ!<8Je!71ZF!<)ot!3uP(1[P,A!<2uu!71ZJ!<4kT!71ZF!<)ot| |!3uP(RI'qR!<2uu!71ZJ!<8Je!71ZF!<)ot!87AP@"AD!;lct| |RK!99rr<&urr=kSrr<&JrrN3#RJ[!a!42\*RIC.U!;lctbl7[lrr<&urrAJd| |rr<&JrrN3#bkqD?!8IMREe+4g!87APRIC.U!;lctbl7[mrr<&trrAJdrr<&J| |rrN3#bkqD?!42\*1[k>D!;lctRK!9:rr<&trr=kSrr<&JrrN3#RJ[!a!42\*| |RIC.U!;lctbl7[mrr<&trrAJdrr<&JrrN3#bkqD?!8IMRFb'Oj!87APRIC.U| |!;lcubl@\Cec,ULrVlkcrVliteGfRMs31B?!!'A*!&O*D!!)or".B2h!7h)L| |!<)ot1]@=R!7_#M!<8Jarr<&*rrAJUrr<&rrr^LFrrCUL!!)ut!1Efc!!(OK| |!W`8Equ6Wrg]%7uJH2SJg&D&?n,E@fqu6cBs8N)Lrr<&trrAJcrr<&LrrW9$| |s31B?!!'A*!&O*D!!)or".B2h!7h)L!<)ot1]@=R!7h)O!<<(equ6WrZi:#n| |n,E@fqu6cBs8N)Lrr<&trrAJcrr<&LrrW9$s31B?!!(dR!-j%pVZ>EM!1E?V| 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|C`:;rF"VtC2s=tES/u`F5)$",UHjk@S\.SD?aD9\i_>(UF9.8p.6s"P"Xn?<| |e/=/Yo>&161Z27(#-==s?klP+l4bdGBfb537&Rg3RHd1IdM,)?RK=0p;h/?N| |2J@QU5JIY"G[m`DS/U-@X(GKj88oln[$R'mVtFN"Lgmo@KWNW3h(%9aX2o$p| |$?9u=P@jUT`R0`+:o%V4kU,/#eeInh85nDK'D\"qkf[mAVL>5&oLL6n(`)A%| |+!k5W2G-/HdN+04_#36=2B-s\4*]]ehrfIJd_,ah2IDRgmfEeZrt`8Q[b9#/| |#>LC:rTNa?2iPd&b;..R-m.]Y_GZa-]N^| |s-m,2[5VWb#BELtn#pGJe#O93o[h=%kn.M\.S[o3ai*nao'5D_\7W4hWshl\| |AB6&c)I?Va[=/j`e:6OS[-nQog&UfB)5t(6>SS7I(0QguAW.hX.Pr]^M@&.^| |X'JA^Nij#-Ur`YFaO6/,@o3\7(eO<;*G2KY<0ek%.KV?B$BXL_RK8O./#K%q| |ZQQk]+f$R*(.g:hO=g$XA;N7.jot&9@+0I(;gDM6^,| |>_7(Hfqk,o_fsGG59V\#4<0Lp-!+\(IkP[+TN<8].C$rlM(Sn)[CT^g[)g7.p`Z*LY| |A0fE,Nn-/:(.i'%=!Z$2kV<^?_(iI,IZ4B:Q/)(=_!CNj@`^V]G,D`]bAYc7| |6?6Sd/Pc:"ZnPm*Vn%LAfJbO$J;N@*`aWR!3bo(!,Y\;3[5(:/F-JNc.$CG-| |7FDmCZm3iio*tR6rs!Du%FDu7cW,t7oS;;G")cruBji5h;h(ks'0ld\,0dpN| |T5D7u_K&S-gZ+gGGG$,70.LVj%-(aTehGB33)5tN!&rfh-OLf/O%Ngl_c%B0| |8T"^)L"ogPM=&T(RmQ7JN0T_.#4:WK(R8cf.,f?Yrb/;?11\[OBXso\g=ajE| |g$ZDnSJBP,/jT4Cd"R3E^/m3+!!!!!8OZBBY!QNJ| |9}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~A(y_1=2*cos(3*x))~p0 0 ~d~Q ]|Expr|[#b @`bb#_b#_b#_})!# b#,["! )b Z# b#," *~: ;.&c54 Third| | try,N We observed that the amplitude needed to be adjusted,N| | So we multiplied by a ,B2,B in front of cos,Hx,I ,L and ,N,N| |,N}& b!( b"0 b#8 b$@ b%H b&P!WW})9# b#,Yes,A The omega graph| | &c54!IS&c54 the same as 2cos,H3x,I,A| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b&L[*! )9# b&L" *~: ;.&c54 `f"} | |i,N In the problems below,L &c54!graph&c54 the mystery function| | first,N}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })6# b&L`f"} ,H| |Mystery functions are named after Greek letters,N,I| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f }) # b&L| |}& b!( b"0 b#8 b$@ b%H b&P!WW})7# b&L`f"} ii,N &c54!Guess&c54 | |a function that might match the mystery function,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f }) # b&L| |}& b!( b"0 b#8 b$@ b%H b&P!WW})># b&L`f"}iii,N Use the "!Times~:!;,Add| | Line Plot: ;. command to &c54!add&c54 the graph of your guess| | }& b!( b"0 b#8 b$@ b%H b&P!WW}`f })b @# b&L`f"} to the | |graph of the mystery function on the same set of axes,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f }) # b&L| |}& b!( b"0 b#8 b$@ b%H b&P!WW})<# b&L`f"}iv,N &c54!Repeat&c54 | |steps 2 and 3 until the graphs of the mystery function | |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })2# b&L`f"} and your guess| | are the same,N}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~T~A(y=alpha(x))~p0 0 ~d~A(y_1=?)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})3# b%4" *~: ;.&c54 Hint,Z a variation| | on the sin,Hx,I function,N}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=pi(x))~p0 0 ~d~A(y_1=?)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}):# b%4" *~: ;.&c54 Hint,Z a variation| | of the ln,Hx,I or log,Hx,I functions,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=beta(x))~p0 0 ~d~A(y_1=?)~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})=# b%4" *~: ;.&c54 Hint,Z a variation| | of the sin,Hx,I function,N Try a phase shift,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~t~p0 0 ~T~A(y=psi(x))~p0 0 ~d~A(y_1=?)~p0 0 ~t~p0 0 ~T~A(y=zeta(x))~p0 0 ~d~A(y_1=?)~p0 0 ~t~p0 0 ~T~A(y=theta(x))~p0 0 ~d~A(y_1=?)~p0 0 ~t~p0 0 ~T~A(y=gamma(x))~p0 0 ~A(y_1=?)~p0 0 ~t~p0 0 ~T~A(y=xi(x))~p0 0 ~A(y_1=?)~p0 0 ~t~p0 0 ~T~A(y=delta(x))~p0 0 ~A(y_1=?)~p0 0 ~t~p0 0 ~T~A(y=rho(x))~p0 0 ~A(y_1=?)~p0 0 ~t~p0 0 ~T~A(y=mu(x))~p0 0 ~A(y_1=?)~p0 0 ~t~p0 0 ~T~A(y=epsilon(x))~p0 0 ~A(y_1=?)~p0 0 ~t~p0 0 ~T~A(y=tau(x))~p0 0 ~A(y_1=?)~p0 0 ~t~p0 0 ~T~A(y=phi(x))~p0 0 ~A(y_1=?)~p0 0 ~t~p0 0 ~T~A(y=lambda(x))~p0 0 ~A(y_1=?)~p0 0 ~t~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4[=! ) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}| |) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}| |) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW})!# b'4`fb#_}" *~: ;bP8&c55*`g| |pc RRc HF| |$75`Q!!!!.!6>-P!riZ/s8Lt2!([(i!([(i!!!!!!"AqL"to<8!$2+@!"&]+| |!!!!.!6>//!!!$!K-1-o!!!!.!6>-?!!E9%!!!!i!!!!i!!!!1!$D7E!!iQ)| |!$D-?!!!!.!6>-?!"OP[JH16$JH16$JH4X/!#C+c| |S,hRKJH4=&ir=Q0fDsq2JH5?C!3LeP[f?L.rI4_G$pX^h:]:6@!!)urNdgp)| |'>=GHs#g>^YQ$0S!5JQ[!!$@*4o>9cIQ[Zos*aqJs+(1A!!**$qu?j#!<<-$| |rW)ou!!)ls&c_q34TGJcs"+3N^]2U[!+,[gqu@"O4TIYFIK0BJJH59A!dcs3CZF?N31d!!n$:!'U@2!!*%M| |!;-^DX[Q)#J^;!!!!K.4o>9cIQ[Zos*aqJs4./g&0![:]LL1s$-SarrDus!.WT#!u:!u:!>!,hi:| |4TKs2s#p5Z!<:UM2XgYW!'i4ls3CZVs5*gks$0E\E"MLiarW)os(XE)2s*la&| |^B"<6IfR7`cbKM[!!#:a^XiGd!.OtJ4TIYFIK0BJ| |ec6;Cs0&'pNr[N+O0AS5!5JPQ5lL`b5l\Uu!#tth>IfKF2!'U@2!!*&M!"k:lYFkiU!71\+YQ'(P^]/7Y+l5Q1OF!"f/.| |"c`Q_If96D^'juAs#g@"!!%HJ!5B!@!"P%h4TKs2s#g?Fs*aqJs4./]&:a0;| |T+CuFTE"A0!!'e65lCZa5l\Uu!#tt!<51^IOtQ7!!$m:!8mfN!'U?F!.OtJ4TIYFIK0BJJH59AqZ-`u!!<51^IOtQ7!!$m:!8mfN!'U?F!.OtJ4TIYFIK0BJJH5?C!#C+c| |S,hRKJH4=&ir=Q0fDsq2JH5?C!"OP[JH16$JH16$JH4X/!"OP[JH16$JH16$| |JH4X/!<3$!| |1''| |b#(-___| |3b2#b.9| 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|:4%7Qdk.JJc_^8?^])D@S`_jb| |N,`NEkg?.q.>k]bqfZR`Amf#>.#KBISB0"$cH40o#]84u6*42bHp7R%qQH#:| |(^uFo,uHLEbi3pDjf/8r=t-G#[9?j;YJ:)5^U)um1rK>T`,cn"| |Pj@6sN>hJ.0)9u5XDu]qH/GA61ipr,>k7b.o\Z^k3[$g$KW5"P!!#SZ:.26O| |@"J@Y| |9}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })%# b'4;bP7&c55)Original Copyright| |,Z }& b!( b"0 b#8 b$@ b%H b&P!WW})3# b'4;,&c54 .I `fb"@}&c54!The| | Finley Press,L 1993`f }&c54 ,L `f"}&c54!All rights reserved`f }&c54 ,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW})*# b'4 705 Lexington Avenue| |}& b!( b"0 b#8 b$@ b%H b&P!WW})+# b'4 Stockton,L CA 95204| |}& b!( b"0 b#8 b$@ b%H b&P!WW}),# b'4 ,H209,I 467,M1320| |}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}| |)4# b'4&c54@Authors&c54 ,Z `f"}&c54%Robert R,N Curtis`f }&c54 | |,F `f"}&c54%Phil R,N Smith`f }&c54 ,N}& b!( b"0 b#8 b$@ b%H b&P!WW}| |) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW})4# b'4This package took| | a lot of time and effort,N }& b!( b"0 b#8 b$@ b%H b&P!WW})6# b'4| |Please pay the shareware fees,N ,HGuilt,L Guilt,L Guilt,I,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW})3# b'4.I `fb"@}&c54!The Finley| | Press,L 1993`f }&c54 ,L `f"}&c54!All rights reserved`f }&c54 ,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~e