document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=760528>Question 760528</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me answer and give some explanations as to how to solve this following question: Which of the following relations are one-to-one? Give reasons.\r<BR>\n" );
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document.write( "1. 2x - 5y =3<BR>\n" );
document.write( "2. y^2 - 3x + 7 =0<BR>\n" );
document.write( "3. y= the squareroot of 5-2x<BR>\n" );
document.write( "4. y= x^3 -2<BR>\n" );
document.write( "5. y= x^2 - 3x +2<BR>\n" );
document.write( "6. y= |3x-5|\r<BR>\n" );
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document.write( "Thank you in advance and please reply as soon as possible since i need time to learn how to arrive at the answers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #462702 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=462702\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A one to one function is a function in which every element in the range of the function corresponds with one and only one element in the domain.\r<BR>\n" );
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document.write( "    Example of 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;\" > function:\r<BR>\n" );
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document.write( "        { (0,1) , (5,2), (6,4) }<BR>\n" );
document.write( "        Domain: 0, 5, 6<BR>\n" );
document.write( "        Range: 1,2, 4\r<BR>\n" );
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document.write( "    Each element in the domain (0, 5, and 6) correspond with a unique element in the range. Therefore this function is a one-to-one function \r<BR>\n" );
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document.write( "If a function is <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;\" >, then the function not only passes the vertical line test (the vertical line test is a way to determine whether or not a relation is a function), but it also passes the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=horizontal ALIGN=MIDDLE  ALT=\"horizontal\"   DISABLED_style= \"max-width:90%; height:auto;\" > line test.\r<BR>\n" );
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document.write( "    The Horizontal Line Test : <BR>\n" );
document.write( "If a horizontal line only intersects with the graph of a function once, then this function is <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;\" >. If a horizontal line intersects the graph of the function more than once, then this function is not <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;\" >. \r<BR>\n" );
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document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+-+5y+=3 ALIGN=MIDDLE  ALT=\"2x+-+5y+=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3%2C3%2C%282%2F5%29x-3%2F5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3%2C3%2C%282%2F5%29x-3%2F5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since a horizontal line only intersects with the graph of a function once, function is <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;\" >\r<BR>\n" );
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document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+-+3x+%2B+7+=0 ALIGN=MIDDLE  ALT=\"y%5E2+-+3x+%2B+7+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3%2C3%2Csqrt%283x-7%29%2C-sqrt%283x-7%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since a horizontal line only intersects with the graph of a function once, function is <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;\" >\r<BR>\n" );
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document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+sqrt%285-2x%29 ALIGN=MIDDLE  ALT=\"y=+sqrt%285-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3%2C3%2Csqrt%285-2x%29%2C-sqrt%285-2x%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since a horizontal line only intersects with the graph of a function once, function is <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;\" >\r<BR>\n" );
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document.write( "4. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+x%5E3+-2 ALIGN=MIDDLE  ALT=\"y=+x%5E3+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3%2C3%2Cx%5E3+-2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3%2C3%2Cx%5E3+-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since a horizontal line only intersects with the graph of a function once, function is <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;\" >\r<BR>\n" );
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document.write( "5. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+x%5E2+-3x+%2B2 ALIGN=MIDDLE  ALT=\"y=+x%5E2+-3x+%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3%2C3%2Cx%5E2+-3x+%2B2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3%2C3%2Cx%5E2+-3x+%2B2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since a horizontal line intersects with the graph of a function twice, function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NOT ALIGN=MIDDLE  ALT=\"NOT\"   DISABLED_style= \"max-width:90%; height:auto;\" > <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;\" >\r<BR>\n" );
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document.write( "6. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+abs%283x-5%29 ALIGN=MIDDLE  ALT=\"y=+abs%283x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3%2C3%2C+abs%283x-5%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3%2C3%2C+abs%283x-5%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since a horizontal line intersects with the graph of a function twice, function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NOT ALIGN=MIDDLE  ALT=\"NOT\"   DISABLED_style= \"max-width:90%; height:auto;\" > <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;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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