document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=899704>Question 899704</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Does y^2 = x^2 - 1 represent y as a function of x? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #545574 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39623)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=545574\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> No.\r<BR>\n" );
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document.write( "Here is why:<BR>\n" );
document.write( "Let x=k, assuming k>=0.\r<BR>\n" );
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document.write( "Solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%28x%5E2-1%29 ALIGN=MIDDLE  ALT=\"y=sqrt%28x%5E2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, although there is a negative branch also; two different functions, but no matter----\r<BR>\n" );
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document.write( "Now, k^2-1>=0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2%3E=1 ALIGN=MIDDLE  ALT=\"k%5E2%3E=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3E=1 ALIGN=MIDDLE  ALT=\"k%3E=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  OR  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3C=-1 ALIGN=MIDDLE  ALT=\"k%3C=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Meaning k must not be an fraction, neither positive nor negative.\r<BR>\n" );
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document.write( "We already took k as positive or zero, so just understand <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3E=1 ALIGN=MIDDLE  ALT=\"k%3E=1\"   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=highlight_green%28y=sqrt%28k%5E2-1%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y=sqrt%28k%5E2-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  will be a value for y.<BR>\n" );
document.write( "You can also choose x=-k and then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%28%28-k%29%5E2-1%29 ALIGN=MIDDLE  ALT=\"y=sqrt%28%28-k%29%5E2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y=sqrt%28k%5E2-1%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y=sqrt%28k%5E2-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is the SAME as for x=k.\r<BR>\n" );
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document.write( "This shows that y gives the same result for x=k and for x=-k.<BR>\n" );
document.write( "Those are two DIFFERENT input values giving the SAME output value.<BR>\n" );
document.write( "NOT a function. </SPAN>\n" );
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