document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120452>Question 120452</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618317953/algebrahomeworkh>Trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find the domain:\r<BR>\n" );
document.write( "\n" );
document.write( "s(y) = 3y/(y+5)\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88280 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=88280\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28y%29=%283y%29%2F%28y%2B5%29 ALIGN=MIDDLE  ALT=\"s%28y%29=%283y%29%2F%28y%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B5=0 ALIGN=MIDDLE  ALT=\"y%2B5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of y that make the denominator zero, then we must exclude them from the domain.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0-5 ALIGN=MIDDLE  ALT=\"y=0-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 5 from both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5 ALIGN=MIDDLE  ALT=\"y=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5 ALIGN=MIDDLE  ALT=\"y=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > makes the denominator equal to zero, this means we must exclude <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5 ALIGN=MIDDLE  ALT=\"y=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > from our domain\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So our domain is:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{\left{y|y\in\mathbb{R} y\neq-5\right}}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "which in plain English reads: y is the set of all real numbers except <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C%3E-5 ALIGN=MIDDLE  ALT=\"y%3C%3E-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So our domain looks like this in interval notation\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(-\infty, -5\right)\cup\left(-5,\infty \right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "note: remember, the parenthesis <font size=4><b>excludes</b></font> -5 from the domain\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If we wanted to graph the domain on a number line, we would get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C50%2C-10%2C10%2C-10%2C10%2C%0D%0Anumber_line%28+500%2C+-15%2C+5%29%2C%0D%0Ablue%28arrow%280.2%2C-7%2C10%2C-7%29%29%2C%0D%0Ablue%28arrow%280.2%2C-6.5%2C10%2C-6.5%29%29%2C%0D%0Ablue%28arrow%280.2%2C-6%2C10%2C-6%29%29%2C%0D%0Ablue%28arrow%280.2%2C-5.5%2C10%2C-5.5%29%29%2C%0D%0Ablue%28arrow%280.2%2C-5%2C10%2C-5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-7%2C-10%2C-7%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-6.5%2C-10%2C-6.5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-6%2C-10%2C-6%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-5.5%2C-10%2C-5.5%29%29%2C%0D%0Ablue%28arrow%28-0.2%2C-5%2C-10%2C-5%29%29%2C%0D%0A%0D%0Acircle%280%2C-5.8%2C0.35%29%2C%0D%0Acircle%280%2C-5.8%2C0.4%29%2C%0D%0Acircle%280%2C-5.8%2C0.45%29%2C%0D%0Acircle%280%2C-5.8%2C0.4%29%2C%0D%0Acircle%280%2C-5.8%2C0.45%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of the domain in blue and the excluded value represented by open circle\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice we have a continuous line until we get to the hole at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5 ALIGN=MIDDLE  ALT=\"y=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is represented by the open circle).<BR>\n" );
document.write( "This graphically represents our domain in which y can be any number except y cannot equal -5<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );