document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=482412>Question 482412</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, my son and I need some serious help with this particular question: Determine whether the relation in the table below is a function, and if so, write a function rule.<BR>\n" );
document.write( "Table reads:<BR>\n" );
document.write( "x    y<BR>\n" );
document.write( "-1   1<BR>\n" );
document.write( "0    2<BR>\n" );
document.write( "2    4<BR>\n" );
document.write( "3    5\r<BR>\n" );
document.write( "\n" );
document.write( "a)yes;f(x)=-1(x)<BR>\n" );
document.write( "b)yes;f(x)=x/2<BR>\n" );
document.write( "c)yes;f(x)=x+2<BR>\n" );
document.write( "d)not a function </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #330290 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=330290\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One way to solve this is graphically.<BR>\n" );
document.write( "Plot the given points (x, y) on a sheet of graph paper on which you drawn the x-axis (horizontal) and the y-axis (vertical).<BR>\n" );
document.write( "You should see a graph like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Cx%2B2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Cx%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To get the corresponding equation, you need to know two things about the line on the graph: its slope (m) and the y-intersection (b).<BR>\n" );
document.write( "The y-intersection is where the line crosses the y-axis and this is at (0, 2) and the slope (m) can be determined by picking any two points on the line and using the following formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can use any two points from the given list, say (-1,1) and (3, 5) as the x's and y's in the formula.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%285-1%29%2F%283-%28-1%29%29 ALIGN=MIDDLE  ALT=\"m+=+%285-1%29%2F%283-%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+4%2F4 ALIGN=MIDDLE  ALT=\"m+=+4%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+1 ALIGN=MIDDLE  ALT=\"m+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > The slope is 1.<BR>\n" );
document.write( "Now use the \"slope-intercept form of a linear equation:<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;\" > and substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+1 ALIGN=MIDDLE  ALT=\"m+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+2 ALIGN=MIDDLE  ALT=\"b+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%2B2 ALIGN=MIDDLE  ALT=\"y+=+x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%2B2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > So yes, it is a function. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );