document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=179816>Question 179816</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question: What similarities and differences do you see between functions and linear equations?\r<BR>\n" );
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document.write( "Are all linear equations functions?\r<BR>\n" );
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document.write( "Please create an equation of a nonlinear function and provide two inputs to evaluate </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #134806 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=134806\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Linear equations or linear functions are a subset of functions. <BR>\n" );
document.write( "Similarities are one unique output for each input and they are continuous by definition.<BR>\n" );
document.write( "Yes, all linear equations are functions.<BR>\n" );
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document.write( "Linear equations take the form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are many ways to make an equation non-linear. <BR>\n" );
document.write( "The simplest may be to change the power of the x exponent.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%5E2%2Bb ALIGN=MIDDLE  ALT=\"y=mx%5E2%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or as an example,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E2-1 ALIGN=MIDDLE  ALT=\"y=2x%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So if I put in x=1,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%281%29-1=1 ALIGN=MIDDLE  ALT=\"y=2%281%29-1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and if I put in x=2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%284%29-1=7 ALIGN=MIDDLE  ALT=\"y=2%284%29-1=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Here's a graph of that non-linear function. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-5%2C+5%2C+-2%2C+8%2C+2x%5E2-1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-5%2C+5%2C+-2%2C+8%2C+2x%5E2-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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