document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=687196>Question 687196</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Draw a picture of each of the functions below, and explain whether or not each is a function, and how you know. (There are 4 graphs with these 4 functions because you also have to draw these functions but I didn't know how to put the graph here)\r<BR>\n" );
document.write( "\n" );
document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2By%5E2=4 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2By%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x%2By=4 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x%2By=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=4 ALIGN=MIDDLE  ALT=\"x%2By=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=4 ALIGN=MIDDLE  ALT=\"xy=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #425096 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=425096\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2By%5E2=4 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2By%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+sqrt%28-%28x-2%29%5E2%2B4%29%2C-sqrt%28-%28x-2%29%5E2%2B4%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "It's the one that has y^2 in it because you could have one x value with two different y values ( a positive and a negative, since y^2 is positive for both).\r<BR>\n" );
document.write( "\n" );
document.write( "If you you use only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28-%28x-2%29%5E2%2B4%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28-%28x-2%29%5E2%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > you wold have a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=semicircle ALIGN=MIDDLE  ALT=\"semicircle\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=function ALIGN=MIDDLE  ALT=\"function\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "On a graph, the idea of single valued means that no vertical line would ever cross more than one value.\r<BR>\n" );
document.write( "\n" );
document.write( "If it crosses more than once it is still a valid curve, but it would not be a function.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C600%2C+++-6%2C+6%2C+-6%2C+6%2C++blue%28line%282%2C6%2C2%2C-6%29%29%2C+grid%280%29%2C%0D%0Agraph%28+600%2C+600%2C+-6%2C+6%2C+-6%2C+6%2Csqrt%28-%28x-2%29%5E2%2B4%29%2C-sqrt%28-%28x-2%29%5E2%2B4%29%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x%2By=4 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x%2By=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2B4x-4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2B4x-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "it is a function\r<BR>\n" );
document.write( "\n" );
document.write( "c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=4 ALIGN=MIDDLE  ALT=\"x%2By=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "d) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=4 ALIGN=MIDDLE  ALT=\"xy=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4%2Fx%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4%2Fx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "this is hyperbola\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "not all hyperbolas are functions, but the one you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=IS ALIGN=MIDDLE  ALT=\"IS\"   DISABLED_style= \"max-width:90%; height:auto;\" > a function It can also be written as:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+4%2Fx+ ALIGN=MIDDLE  ALT=\"y+=+4%2Fx+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "the ones that are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NOT ALIGN=MIDDLE  ALT=\"NOT\"   DISABLED_style= \"max-width:90%; height:auto;\" > functions are in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fa%5E2+-+y%5E2%2Fb%5E2+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2Fa%5E2+-+y%5E2%2Fb%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >; whenever <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=squared ALIGN=MIDDLE  ALT=\"squared\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you do <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+have ALIGN=MIDDLE  ALT=\"+have\"   DISABLED_style= \"max-width:90%; height:auto;\" > a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=functions ALIGN=MIDDLE  ALT=\"functions\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );