document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=262805>Question 262805</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the domain and range of the following function\r<BR>\n" );
document.write( "\n" );
document.write( "f(x) = 8/X+9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #193594 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=193594\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> assuming you mean f(x) = 8 / (x+9), then:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the domain is all real values of x except x = -9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x = -9, then the denominator is 0 and the range is undefined.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "every value in the domain must lead to one or more values in the range or the domain is not valid.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the domain of this equation is valid except at x = -9.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the range is all real values of y except 0 since y can approach 0 but will never actually be 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the limit of y as x approaches infinity = 0, however, so there is a horizontal asymptote at y = 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "there is also a vertical asymptote at x = -9.   as x approaches -9, the value of y approaches  +/- infinity.   at x = -9, the value of y is undefined.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "graph of y = 8 / (x+9) is shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28600%2C600%2C-20%2C20%2C-20%2C20%2C8%2F%28x%2B9%29%29 ALIGN=MIDDLE  ALT=\"graph+%28600%2C600%2C-20%2C20%2C-20%2C20%2C8%2F%28x%2B9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you draw a vertical line at x = -9, you will see that the value of y approaches it but never touches it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you draw a horizontal line at y = 0, you will see that the value of y approaches it but never touches it.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );