document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=662037>Question 662037</A>: <I><SPAN STYLE=\"word-break: break-all;\"> {(1,-1),(0,0),(3,-3),(-2,2)} is this relation a function? Why? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #411909 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=411909\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> {(1,-1),(0,0),(3,-3),(-2,2)} \r<BR>\n" );
document.write( "\n" );
document.write( "There are 2 ways to check this. \r<BR>\n" );
document.write( "\n" );
document.write( "1. make a graph and plot out all the coordinates, and if one point is on exactly on top of another, it is not a function\r<BR>\n" );
document.write( "\n" );
document.write( "If it isn't, then it is a function (it's vertical line test)\r<BR>\n" );
document.write( "\n" );
document.write( "2.<BR>\n" );
document.write( " look at all the x's (1st number) and see if any are the same: <BR>\n" );
document.write( "we have 1,0. 3,and -2- none of them repeat so this is automatically a function\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now lets look at the inverse<BR>\n" );
document.write( " <BR>\n" );
document.write( "since our y's become x's, lets look at the y's in the original function: we have -1, 0, -3, and 2 \r<BR>\n" );
document.write( "\n" );
document.write( "none of them repeat \r<BR>\n" );
document.write( "\n" );
document.write( "however, it the two points had the same y's, it would still be a function\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here is a graph;\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=find_equation_of_line.solver>FIND EQUATION of straight line given 2 points</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (1, -1) and (x2, y2) = (3, -3).<BR>\n" );
document.write( "  Slope a is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%28-3--1%29%2F%283-1%29+=+-1 ALIGN=MIDDLE  ALT=\"a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%28-3--1%29%2F%283-1%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  Intercept is found from equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ax%5B1%5D%2Bb+=+y%5B1%5D ALIGN=MIDDLE  ALT=\"a%2Ax%5B1%5D%2Bb+=+y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2A1+%2Bb+=+0 ALIGN=MIDDLE  ALT=\"-1%2A1+%2Bb+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. From that, <BR>\n" );
document.write( "  intercept b is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=y%5B1%5D-a%2Ax%5B1%5D ALIGN=MIDDLE  ALT=\"b=y%5B1%5D-a%2Ax%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-1--1%2A1+=+0 ALIGN=MIDDLE  ALT=\"b=-1--1%2A1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  y=(-1)x + (0)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Your graph:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++drawing%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A++++graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+-1%2Ax%2B0+%29%2C%0D%0A++++red%28+locate%28+1%2C+-1%2C+%221%2C+-1%22+%29%2C+circle%28+1%2C+-1%2C+0.15+%29+%29%2C%0D%0A++++green%28+locate%28+3%2C+-3%2C+%223%2C+-3%22+%29%2C+circle%28+3%2C+-3%2C+0.15+%29+%29%0D%0A++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );