document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=232438>Question 232438</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have tried to get help on this problem for a while and nobody is able to help me.  I have 2 different problems, but I post them seperately.\r<BR>\n" );
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document.write( "Evaluate the exponential equation for three positive values of x, three negaitve values of x, and at x=0.  Show all work and please write out the steps on what you are doing so I can learn from it.  Use the resulting ordered pairs to plot the graph.  State the equation of theline asymptotic to the graph (if any)\r<BR>\n" );
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document.write( "Problem:(1/4)^x -3, this is worth 10 ponts out of 30, so if I don't get this I am in trouble.  Please help me.  If has been 16 years since I've done this and my professor isn't much help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #171832 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=171832\">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( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ \left(\frac{1}{4}\right)^{x-3}\">.\r<BR>\n" );
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document.write( "Evaluate:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(3),\,f(2),\,f(1),\,f(0),\,f(-1),\,f(-2),\,f(-3)\">\r<BR>\n" );
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document.write( "I'll do three of these for you:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(3)\ =\ \left(\frac{1}{4}\right)^{(3)-3}\ =\ \left(\frac{1}{4}\right)^{0}\ =\ 1\">.\r<BR>\n" );
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document.write( "So the ordered pair is (3, 1)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(1)\ =\ \left(\frac{1}{4}\right)^{(1)-3}\ =\ \left(\frac{1}{4}\right)^{-2}\ =\ 4^2 = 16\">.\r<BR>\n" );
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document.write( "So the ordered pair is (1, 16)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(-2)\ =\ \left(\frac{1}{4}\right)^{(-2)-3}\ =\ \left(\frac{1}{4}\right)^{-5}\ =\ 4^5 = 1024\">.\r<BR>\n" );
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document.write( "So the ordered pair is (-2,1024)\r<BR>\n" );
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document.write( "I presume you know how to plot points.  Once you have done all the required arithmetic and plotted your set of points, draw a smooth curve.  It should look something like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28%0D%0A500%2C+500%2C+-2%2C+8%2C+-2%2C+18%2C%0D%0Agrid%281%29%2C%0D%0Ablue%28circle%281%2C16%2C.1%29%29%2C%0D%0Ablue%28circle%283%2C1%2C.1%29%29%2C%0D%0Ablue%28circle%282%2C4%2C.1%29%29%2C%0D%0Ablue%28circle%284%2C.25%2C.1%29%29%2C%0D%0Agraph%28%0D%0A500%2C+500%2C+-2%2C+8%2C+-2%2C+18%2C%0D%0A%281%2F4%29%5E%28x-3%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice that no matter how large you make <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">, the value of the function will never be exactly zero.  It gets very close, very fast, but never quite makes it.  Therefore asymptotic to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y = 0\">, in other words, to the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-axis.\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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