document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=939658>Question 939658</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I was hoping to get some help I took this problem from my book, I have homework problems that are the same can some one show me how to work this?\r<BR>\n" );
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document.write( "For each set of ordered pairs, determine if the set is a function, a one-to-one function, or neither. Reverse all the ordered pairs in each set and determine if this new set is a function, a one-to-one function, or neither.\r<BR>\n" );
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document.write( "{(1, 2), (2, 1), (3, 4), (4, 3)} </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #572639 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=572639\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To have a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=function ALIGN=MIDDLE  ALT=\"function\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the pairs, of the form (x,y),<BR>\n" );
document.write( "must be such that each x is paired with only one y.<BR>\n" );
document.write( "To have a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28one-to-one%29 ALIGN=MIDDLE  ALT=\"red%28one-to-one%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=function ALIGN=MIDDLE  ALT=\"function\"   DISABLED_style= \"max-width:90%; height:auto;\" > , you need pairs, of the form (x,y),<BR>\n" );
document.write( "That form a function (see above),<BR>\n" );
document.write( "and also such that each y is paired with only one x.<BR>\n" );
document.write( "If you have a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=one-to-one ALIGN=MIDDLE  ALT=\"one-to-one\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=function ALIGN=MIDDLE  ALT=\"function\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "reversing the pairs you get another one-to-one function.<BR>\n" );
document.write( "Also, if reversing the pairs of a function you get another function,<BR>\n" );
document.write( "both functions are one-to-one functions,<BR>\n" );
document.write( "and we say that each of the two functions is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=inverse ALIGN=MIDDLE  ALT=\"inverse\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the other function.<BR>\n" );
document.write( "That is a lot of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=names ALIGN=MIDDLE  ALT=\"names\"   DISABLED_style= \"max-width:90%; height:auto;\" > to remember, and I am sorry that you have to go through this. (I am also glad I don't have to remember those names any more).<BR>\n" );
document.write( " <BR>\n" );
document.write( "Is the given set a function?<BR>\n" );
document.write( "The first members of each pair form the set {1,2,3,4} .<BR>\n" );
document.write( "Since the first numbers in the pairs are all different,<BR>\n" );
document.write( "you do not have the same x shown twice, paired with different y's.<BR>\n" );
document.write( " <BR>\n" );
document.write( "After you reverse all the ordered pairs, is the new set a function?<BR>\n" );
document.write( "Reversing the pairs you end up with<BR>\n" );
document.write( "{ (2,1) , (1,2) , (4,3) , (3,4) }.<BR>\n" );
document.write( "Thee new first members of each pair form the set {2,1,4,3} .<BR>\n" );
document.write( "Again, those x values are all different,<BR>\n" );
document.write( "so there is no danger of having the same one paired with two different y values.<BR>\n" );
document.write( "The new set is also a function.<BR>\n" );
document.write( " <BR>\n" );
document.write( "The original set and the reversed set are both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=one-to-one ALIGN=MIDDLE  ALT=\"one-to-one\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=functions ALIGN=MIDDLE  ALT=\"functions\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "MORE NAMES:<BR>\n" );
document.write( "Maybe you were taught a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertical-line-test ALIGN=MIDDLE  ALT=\"vertical-line-test\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find if a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=relation ALIGN=MIDDLE  ALT=\"relation\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "meaning a set of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ordered-pairs%28x%2Cy%29 ALIGN=MIDDLE  ALT=\"ordered-pairs%28x%2Cy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , is a function,<BR>\n" );
document.write( "and a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=horizontal-line-test ALIGN=MIDDLE  ALT=\"horizontal-line-test\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find if it is also a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=one-to-one ALIGN=MIDDLE  ALT=\"one-to-one\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=function ALIGN=MIDDLE  ALT=\"function\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Those go like this:<BR>\n" );
document.write( "1) You plot your ordered pairs as points on an x-y chart.<BR>\n" );
document.write( "I plotted your points (circled in green) below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-0.5%2C4.5%2C-0.5%2C4.5%2C%0D%0Agrid%282%29%2Cgreen%28circle%281%2C2%2C0.1%29%29%2C%0D%0Agreen%28circle%282%2C1%2C0.1%29%29%2Cgreen%28circle%283%2C4%2C0.1%29%29%2C%0D%0Agreen%28circle%284%2C3%2C0.1%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2) If there is no way to \"skewer\" two or more of the points with a vertical line,<BR>\n" );
document.write( "your relation is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=function ALIGN=MIDDLE  ALT=\"function\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertical-line-test ALIGN=MIDDLE  ALT=\"vertical-line-test\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "3) If there is also no way to \"skewer\" two or more of the points with a horizontal line,<BR>\n" );
document.write( "your relation is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=one-to-one ALIGN=MIDDLE  ALT=\"one-to-one\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=function ALIGN=MIDDLE  ALT=\"function\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=horizontal+-line-test ALIGN=MIDDLE  ALT=\"horizontal+-line-test\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "NOTE: I do not believe they should make you memorize all those names in math class.<BR>\n" );
document.write( "You have to memorize enough stuff in the other classes, and memorizing makes math boring.<BR>\n" );
document.write( "I think math is a lot of fun, and I use all the time<BR>\n" );
document.write( "it to solve real life problem,<BR>\n" );
document.write( "and to satisfy my curiosity about puzzling stuff that is not a problem to me<BR>\n" );
document.write( "(like the problems in this website).<BR>\n" );
document.write( "Unfortunately, I am not a teacher,<BR>\n" );
document.write( "and they would not let me be one,<BR>\n" );
document.write( "because I am not good enough at boring students to tears. </SPAN>\n" );
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