document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=433498>Question 433498</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph f(x)=(3^-x)-2 and determine the domain, range and vertical asymptote of f.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #300499 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=300499\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Graph f(x)=(3^-x)-2 and determine the domain, <BR>\n" );
document.write( "range and vertical asymptote of f. <BR>\n" );
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document.write( "f(x) = 3^(-x) - 2<BR>\n" );
document.write( "f(x) = (1/3)^x -2<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%2C400%2C300%2C-5%2C20%2C-5%2C10%2C3%5E%28-2x%29%29 ALIGN=MIDDLE  ALT=\"graph%2C400%2C300%2C-5%2C20%2C-5%2C10%2C3%5E%28-2x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Domain: All Real Numbers<BR>\n" );
document.write( "Explanation: The domain of a function is \"all Real<BR>\n" );
document.write( "Numbers\" unless there is some pattern in its rule<BR>\n" );
document.write( "which excludes certain numbers.  Examples are:<BR>\n" );
document.write( "1. a variable expression in the denominator which<BR>\n" );
document.write( "could cause the denominator to be zero; <BR>\n" );
document.write( "2. an even-root expression with a variable that<BR>\n" );
document.write( "could cause the radicand to be negative;<BR>\n" );
document.write( "3. a randical expression in a log or ln term that<BR>\n" );
document.write( "could be negative or zero.<BR>\n" );
document.write( "If none of these are present in the rule of a function,<BR>\n" );
document.write( "the Domain is \"All Real Numbers\".\r<BR>\n" );
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document.write( "Range: y>= -2<BR>\n" );
document.write( "Explanation: 3^-x = (1/3)^x has a minimum value of zero.<BR>\n" );
document.write( "So y will have a minimum value of -2.<BR>\n" );
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document.write( "Vertical Asympt: none<BR>\n" );
document.write( "Explanation: There is no variable expression in a denominator.<BR>\n" );
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document.write( "Horizontal Asympt: y = -2<BR>\n" );
document.write( "Explanation: As x approaches infinity, (1/3)^x approaches<BR>\n" );
document.write( "zero, so y approaches -2.\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "  </SPAN>\n" );
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