document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=505848>Question 505848</A>: <I><SPAN STYLE=\"word-break: break-all;\">   Please, help me solving it...<BR>\n" );
document.write( "  Use interval notation to write the domain of f:<BR>\n" );
document.write( "f(x)= x-1\3x + 6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #339986 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=339986\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (x-1) / (3x+6)<BR>\n" );
document.write( "the denominator will be 0 when x = -2.<BR>\n" );
document.write( "the domain will be all real values of x except x = -2.<BR>\n" );
document.write( "this would show up as:<BR>\n" );
document.write( "(-infinity,-2) union (-2,infinity)<BR>\n" );
document.write( "this reads:<BR>\n" );
document.write( "x is smaller than -2, or x is greater than -2, but x is not equal to -2.<BR>\n" );
document.write( "a graph of this equation is shown below:<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%2C%28x-1%29%2F%283x%2B6%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C%28x-1%29%2F%283x%2B6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you can see that, at x = -2, there is a vertical asymptote.<BR>\n" );
document.write( "as x approaches -2 from the left side, the value of y approaches  minus infinity.<BR>\n" );
document.write( "as x approaches -2 from the right side, the value of y approaches infinity.<BR>\n" );
document.write( "x can never be equal to -2 because y can never be equal to infinity because infinity is not a number.<BR>\n" );
document.write( "the domain of the equation is  represented by the value of x.<BR>\n" );
document.write( "the range of the equation is represented by the value of y.<BR>\n" );
document.write( "the value in the domain has to lead to a real value in the range.<BR>\n" );
document.write( "while -2 is a real value, it cannot lead to a real value in the range because the value of anything divided by 0 is undefined.<BR>\n" );
document.write( "when x = -2, the value of the denominator becomes 3*(-2) + 6 which which becomes 6 - 6 which equals 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );