document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=142579>Question 142579</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here is my \"domain\" problem if it makes any sense:<BR>\n" );
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document.write( "  Find domain of the function y=2sqrt of 4x+10\r<BR>\n" );
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document.write( "Teresa M. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103781 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=103781\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%284x%2B10%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%284x%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "Remember you cannot take the square root of a negative value. So that means the argument <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B10 ALIGN=MIDDLE  ALT=\"4x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be greater than or equal to zero \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B10%3E=0 ALIGN=MIDDLE  ALT=\"4x%2B10%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the inner expression greater than or equal to zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%3E=0-10 ALIGN=MIDDLE  ALT=\"4x%3E=0-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 10 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%3E=-10 ALIGN=MIDDLE  ALT=\"4x%3E=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=%28-10%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x%3E=%28-10%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 4 to isolate x \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=-5+%2F+2 ALIGN=MIDDLE  ALT=\"x%3E=-5+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So that means x must be greater than or equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+%2F+2 ALIGN=MIDDLE  ALT=\"-5+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in order for x to be in the domain\r<BR>\n" );
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document.write( "So the domain in set-builder notation is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{\left{x|x\ge -\frac{5}{2}\right}}\">\r<BR>\n" );
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document.write( "So here is the domain in interval notation: [<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+%2F+2 ALIGN=MIDDLE  ALT=\"-5+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \infty\">)\r<BR>\n" );
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document.write( "Notice if we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2Asqrt%284x%2B10%29 ALIGN=MIDDLE  ALT=\"y=2%2Asqrt%284x%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+2%2Asqrt%284x%2B10%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+2%2Asqrt%284x%2B10%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > notice how the graph never crosses the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5+%2F+2 ALIGN=MIDDLE  ALT=\"x=-5+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this graphically verifies our answer.\r<BR>\n" );
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document.write( "and we can see that x must be greater than or equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5+%2F+2 ALIGN=MIDDLE  ALT=\"-5+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in order to lie on the graph<BR>\n" );
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