document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199064>Question 1199064</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether this relation defines a function (Could you show the work Im struggling with this problem)\r<BR>\n" );
document.write( "\n" );
document.write( "x-4y=8  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832755 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=832755\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Use the graphing tool Desmos to type in exactly what is given.<BR>\n" );
document.write( "It will produce a straight line as shown in this link.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.desmos.com/calculator/pp87lovs1g\">https://www.desmos.com/calculator/pp87lovs1g</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In case you're not able to visit the link, this is what the screenshot would look like (similar to it)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-100%2C%288-x%29%2F%28-4%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-100%2C%288-x%29%2F%28-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To see if we have a function or not, we use the vertical line test.<BR>\n" );
document.write( "This is where we try to pass a single vertical line through more than one point on the green line above. <BR>\n" );
document.write( "As you can probably tell, it is impossible to draw such a vertical line. <BR>\n" );
document.write( "Each vertical line goes through *exactly* one and only one point on the green line. <BR>\n" );
document.write( "This means each input (x) leads to exactly one output (y).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In short: one input ---> one output\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Therefore, this graph passes the vertical line test and we have a function.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here's an example of a non-function<BR>\n" );
document.write( "x^2+y^2 = 25<BR>\n" );
document.write( "This plots out a circle of radius 5, centered at the origin<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-10%2C10%2C-10%2C10%2C%0D%0Agraph%28400%2C400%2C-10%2C10%2C-10%2C10%29%2C%0D%0Agreen%28circle%280%2C0%2C5%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now it is fairly clear that we can pass a single vertical line through more than one point on the green curve. <BR>\n" );
document.write( "For example, we can pass a vertical line through x = 0 to have it intersect at (0,5) and (0,-5)<BR>\n" );
document.write( "This leads to the graph failing the vertical line test and we don't have a function.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Another example of a non-function<BR>\n" );
document.write( "x = y^2<BR>\n" );
document.write( "This produces a sideways parabola opening to the right<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-100%2Csqrt%28x%29%2C-sqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-100%2Csqrt%28x%29%2C-sqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The upper and lower pieces (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%28x%29 ALIGN=MIDDLE  ALT=\"-sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > respectively) combine to form the entire curve treated as one single entity. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I recommend you typing these examples into Desmos to interact with the graph. I also recommend exploring other examples of functions and non-functions. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "GeoGebra is a similar graphing tool that I use all the time as well. Both graphing tools are free.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );