document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=642585>Question 642585</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the equation represents y as a function of x.<BR>\n" );
document.write( "x^2+y^2=4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #404180 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=404180\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A relation is not a function if it assigns more than one y value to any x value in its domain.<BR>\n" );
document.write( "For x=0, the equation gives us y=2 and y=-2.<BR>\n" );
document.write( "That is enough to say that the equation does not represent y as a function of x.<BR>\n" );
document.write( "In fact, the equation represents a circle centered at (0,0) with radius 2.<BR>\n" );
document.write( "For any x such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%3Cx%3C2 ALIGN=MIDDLE  ALT=\"-2%3Cx%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the equation assigns two values of y.<BR>\n" );
document.write( "If you just had the graph corresponding to that equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-3%2C3%2C-3%2C3%2C%0D%0Agrid%281%29%2C%0D%0Ablue%28circle%280%2C0%2C2%29%29%2C%0D%0Agreen%28line%280.5%2C-3%2C0.5%2C3%29%29%2C%0D%0Alocate%280.6%2C1%2Cx=0.5%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you would know that it is not a function because there is a vertical line x=k that crosses the graph at two points.<BR>\n" );
document.write( "(There is really an infinite number of such lines, but one is enough to prove it's not a function). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );