document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1037247>Question 1037247</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sketch a graph of a function f that satisfies the following conditions: \r<BR>\n" );
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document.write( "f does NOT have an inverse function \r<BR>\n" );
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document.write( "f(x) > x for all x \r<BR>\n" );
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document.write( "f(1) > 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #652589 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=652589\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E2+-+x+%2B+3 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E2+-+x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "f has no inverse function since it fails the horizontal line test for one-to-one-ness.<BR>\n" );
document.write( "f(x) > x since, for all real x, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x%2B3+%3E0 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2B3+%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%5E2+-+x+%2B+3+%3E+x ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%5E2+-+x+%2B+3+%3E+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Finally f(1) = 3 > 0.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E2+-+x+%2B3%2C+x+%29 ALIGN=MIDDLE  ALT=\"graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E2+-+x+%2B3%2C+x+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "(Notice that the parabola is entirely above the line y = x, which signifies f(x) > x for all x.)\r<BR>\n" );
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document.write( "There still many more functions that would satisfy the initial conditions. </SPAN>\n" );
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