document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=284166>Question 284166</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Im haveing trubles with the problem { if f(x)=-1, find the domain and range of function  f }   THANK YOU  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #206192 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=206192\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "The domain of a function is the set of all numbers that the independent variable can assume and have the function be defined.  In your case, it doesn't matter what value you select for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">, the function will always be defined because it always has a value of -1.  Therefore, the domain of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f\"> is all real numbers.  There are a couple of ways to express that, other than just saying it:\r<BR>\n" );
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document.write( "In set builder notation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \{x\,|\,x\,\in\,\R\}\">\r<BR>\n" );
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document.write( "In interval notation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(-\infty,\,\infty\right)\">\r<BR>\n" );
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document.write( "The range of a function is the set of all values that the function can assume for every possible value in the domain.  In this case, for every real number input to your function, the value of the function is -1.  Therefore the range is the number -1.\r<BR>\n" );
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document.write( "In set notation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \{-1\}\">\r<BR>\n" );
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document.write( "or set builder notation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \{y\,|\,y\ =\ -1\}\">\r<BR>\n" );
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document.write( "And interval notation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left[-1,\,-1\right]\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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