document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=22834>Question 22834</A>: <I><SPAN STYLE=\"word-break: break-all;\">   I believe this would be the best place to ask...Okay, this is a relation (set of ordered pairs) that I have to write an equation for. The set is :\r<BR>\n" );
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document.write( "(-3,10)(-2,5)(-1,2)(0,1)(1,2)(2,5)(3,10)\r<BR>\n" );
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document.write( "x : -3, -2, -1, 0, 1, 2, 3<BR>\n" );
document.write( "y : 10, 5, 2, 1, 2, 5, 10\r<BR>\n" );
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document.write( "I'm supposed to divide the range differences by the domain differences :\r<BR>\n" );
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document.write( "range difference : 5, 3 1<BR>\n" );
document.write( "domain difference : 1\r<BR>\n" );
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document.write( "But, if I divide 5/1, 3/1 and 1/1, I end up with 5, 3 and 1, as any number divided by 1 is that number. So where do I go from here and how do I get there??? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #11274 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=11274\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I believe this would be the best place to ask...Okay, this is a relation (set of ordered pairs) that I have to write an equation for. The set is : <BR>\n" );
document.write( "SEE MY COMMENTS BELOW<BR>\n" );
document.write( "(-3,10)(-2,5)(-1,2)(0,1)(1,2)(2,5)(3,10)…OK <BR>\n" );
document.write( "x : -3, -2, -1, 0, 1, 2, 3………GOOD<BR>\n" );
document.write( "y : 10, 5, 2, 1, 2, 5, 10 ………GOOD<BR>\n" );
document.write( "I'm supposed to divide the range differences by the domain differences :THIS IS HINT GIVEN TO HELP YOU..OK… <BR>\n" );
document.write( "range difference : 5, 3 1…THIS IS NOT CORRECT.IT IS A GOOD PRACTICE TO FOLLOW AN ORDER OR CONVENTION.SUBTRACT PREVIOUS ENTRY FROM SUCCEEDING ENTRY ALWAYS.SO THE RANGE DIFFERENCE IS –5,-3,-1,1,3,5.<BR>\n" );
document.write( "domain difference : 1 ..CONSTANT ALWAYS..GOOD.HERE YOU FOLLOWED THE CONVNTION I MENTIONED ABOVE<BR>\n" );
document.write( "But, if I divide 5/1, 3/1 and 1/1, I end up with 5, 3 and 1, as any number divided by 1 is that number…OK ..BUT YOU GET –5,-3,-1,1,3,5 AS WE CORRECTED ABOVE.<BR>\n" );
document.write( " So where do I go from here and how do I get there???…LOOK AT THE OBJECTIVE..WE HAVE TO FIND A PATTERN..A HINT IS GIVEN..WE USED THE HINT AND GOT THE NUMBERS AS –5,-3,-1,1,3,5…THERE IS A PATTERN HERE..THEY STARTED WITH –5 AND INCREASED BY A CONSTANT DIFFERENCE OF 2 ..THAT GIVES US THE CLUE TO DERIVE THE RELATION<BR>\n" );
document.write( "LET US CALL THE FIRST NUMBER AS X AS YOU NAMED IT .SECOND NUMBER IS Y.<BR>\n" );
document.write( "SO WE GOT (X1,Y1),(X2,Y2)…ETC<BR>\n" );
document.write( "AND NOW YOU HAVE TO FIND A RELATION  BETWEEN X AND Y BY ANALYSING THEM SEPERATELY OR TOGETHER BY COMBINING THEM<BR>\n" );
document.write( "LET ME SHOW YOU BOTH METHODS.<BR>\n" );
document.write( "FIRSTLY LET US ANALYSE SEPERATELY.WE IND THAT BOTH ARE LINKED TO N THE NUMBER OF THE TERM.SO LET US TRY TO RELATE EACH WITH N WHICH WILL THEN GIVE US WHAT IS CALLED AS PARAMETRIC RELATION.THAT IS X IS RELATED TO N AND Y IS RELATED TO N .SO INDIRECTLY X AND Y ARE RELATED THROUGH A PARAMETER N.<BR>\n" );
document.write( "LET US TAKE UP X FIRST.WE  FOUND<BR>\n" );
document.write( "X2-X1=1<BR>\n" );
document.write( "X3-X2=1<BR>\n" );
document.write( "X4-X3=1<BR>\n" );
document.write( "X5-X4=1<BR>\n" );
document.write( "Etc…..<BR>\n" );
document.write( "X(N+1)-X(N)=1\r<BR>\n" );
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document.write( "LET US ADD THEM ALL TOGETHER..WE FIND THAT X2,X3,X4…X(N) CANCEL OUT LEAVING ONLY X(N+1)-X1 ON THE L.H.S…ON THE R.H.S. WE GET 1+1+1…N TIMES =1*N=N<BR>\n" );
document.write( "HENCE WE GET X(N+1)-X1=N<BR>\n" );
document.write( "BUT X1=-3…SO ….X(N+1)=N+X1=N-3..WE CAN CHECK BCK BY PUTTING N=0,1,2,3,…..ETC…WE GET X(0+1)=X1= 0-3,….X(1+1)=X2=1-3=-2…ETC..OK.<BR>\n" );
document.write( "NOW LET US SEE Y ,WE FOUND<BR>\n" );
document.write( "Y2-Y1=-5<BR>\n" );
document.write( "Y3-Y2=-3<BR>\n" );
document.write( "Y4-Y3=-1<BR>\n" );
document.write( "Y5-Y4=1<BR>\n" );
document.write( "Y6-Y5=3<BR>\n" );
document.write( "Y7-Y6=5<BR>\n" );
document.write( "ETC…..<BR>\n" );
document.write( "Y(N+1)-YN= -5 +(N-1)*2= -5+2N-2=2N-7…….LET ME EXPLIN THIS TO YOU.WE FIND THE NUMBERS ON THE R.H.S ARE –5,-3,-1 ETC….DIFFERING BY A CONSTANT VALUE 2..THIS IS CALLED ARITHMATIC PROGRESSION(A.P)……. 2 ND TERM I OBTAINED BY ADDING 2 O THE FIRT TERM .THIRD TERM IS GOT BY ADDING 2*2 TO THE FIRST TERM.FOURTH IS OBTAINED BY ADDING 2*3 TO THE FIRST TERM……N TH TERM IS OBTAINED BY ADDING (N-1)*2 TO THE FIRST TERM<BR>\n" );
document.write( "THE FORMULAE ARE …NTH TERM =TN=A+(N-1)*D WHERE A IS THE FIRST TERM AND D IS THE CONSTANT DIFFERENCE.<BR>\n" );
document.write( "SUM OF N TERMS OF AN A.P. IS GIVEN BY <BR>\n" );
document.write( "SN=(N/2){2A+(N-1)*D}…WHICH WE SHALL USE BELOW<BR>\n" );
document.write( "NOW AS WE DID EARLIER LET US ADD ALL THE ABOVE TO GET<BR>\n" );
document.write( "Y(N+1)-Y1={-5+(-3)+(-1)+1+3………..+(2N-7)}=AS PER THE FORMULA ABOVE<BR>\n" );
document.write( "Y(N+1)-Y1=(N/2){2*(-5)+(N-1)*2}=(N/2){-10+2N-2}=(N/2)(2N-12)<BR>\n" );
document.write( "=(N/2)2(N-6)=N(N-6)=N^2-6N….BUT Y1=10 SO WE GET <BR>\n" );
document.write( "Y(N+1)-Y1=Y(N+1)-10=N^2-6N….OR…….<BR>\n" );
document.write( "Y(N+1)=N^2-6N+10……LET US CHECK BACK BY PUTTING N+0,1,2,ETC….<BR>\n" );
document.write( "Y(0+1)=Y1=0-0+10=10…OK<BR>\n" );
document.write( "Y(1+1)=Y2=1-6+10=5…..OK<BR>\n" );
document.write( "Y(2+1)=Y3=2^2-6*2+10=2……OK<BR>\n" );
document.write( "Y(3+1)=Y4=3^2-6*3+10=1…….OK<BR>\n" );
document.write( "Y(4+1)=Y5=4^2-6*4+10=2………OK<BR>\n" );
document.write( "Y(5+1)=Y6=5^2-6*5+10=5…….OK<BR>\n" );
document.write( "Y(6+1)=Y7=6^2-6*6+10=10…OK…<BR>\n" );
document.write( "SO NOW WE GOT …Y(N+1)=N^2-6N+10<BR>\n" );
document.write( "THIS TOGETHER WITH X(N+1)=N-3….GIVES US THE RELATION BETWEEN X AND Y IN TERMS OF ACOMMON PARAMETER N.<BR>\n" );
document.write( "NOW IF WE WANT X AND Y DIRECTLY RELATED WE HAVE TO ELIMINATE N ..WE NOTE THAT X(N+1)=N-3…OR N=X(N+1)+3…BY PUTTING THIS IN EQUATION FOR Y(N+1)=N^2-6N+10,WE GET A DIRET RELATION BETWEEN X AND Y …<BR>\n" );
document.write( "Y(N+1)={X(N+1)+3}^2-6{X(N+1)+3}+10<BR>\n" );
document.write( "IF YOU ARE MORE COMFORTABLE WITH XN AND YN YOU CAN WRITE THE ABOVE AS <BR>\n" );
document.write( "YN=(XN+3)^2-6(XN+3)+10......OR IN CONVENTIONAL FORM WE CAN WRITE THIS AS <BR>\n" );
document.write( "Y=(X+3)^2-6(X+3)+10=X^2+9+6X-6X-18+10=X^2+1...OR<BR>\n" );
document.write( "Y=X^2+1.....YOU CAN CHECK ALL THE ORDERED PAIRS AND THEY SATISFY THIS EQUATION </SPAN>\n" );
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