document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=763502>Question 763502</A>: <I><SPAN STYLE=\"word-break: break-all;\"> determine whether the equation defines y as a function of x <BR>\n" );
document.write( "y=x2 and x=y2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #464847 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=464847\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Functions can only have one <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-value ALIGN=MIDDLE  ALT=\"y-value\"   DISABLED_style= \"max-width:90%; height:auto;\" > per <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-value ALIGN=MIDDLE  ALT=\"x-value\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2 ALIGN=MIDDLE  ALT=\"y=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a function; works because it has two <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-values ALIGN=MIDDLE  ALT=\"x-values\"   DISABLED_style= \"max-width:90%; height:auto;\" > per <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   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=x=y%5E2 ALIGN=MIDDLE  ALT=\"x=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%28x%29 ALIGN=MIDDLE  ALT=\"-sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >; it's not a function because has two <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-values ALIGN=MIDDLE  ALT=\"y-values\"   DISABLED_style= \"max-width:90%; height:auto;\" > per <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which, for functions, is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=against ALIGN=MIDDLE  ALT=\"against\"   DISABLED_style= \"max-width:90%; height:auto;\" > the rules \r<BR>\n" );
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document.write( "This will make sense if you graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2 ALIGN=MIDDLE  ALT=\"y=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%5E2 ALIGN=MIDDLE  ALT=\"x=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > side by side.<BR>\n" );
document.write( "Now try the \"vertical line test\".\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28600%2C600%2C+-10%2C+10%2C+-10%2C+10%2C++blue%28line%282%2C10%2C2%2C-10%29%29%2Cgraph%28+600%2C600%2C+-10%2C+10%2C+-10%2C+10%2Csqrt%28x%29%2C-sqrt%28x%29%2C+x%5E2%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "as you can see, the vertical line intersects <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%5E2 ALIGN=MIDDLE  ALT=\"x=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in two points </SPAN>\n" );
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