document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=270116>Question 270116</A>: <I><SPAN STYLE=\"word-break: break-all;\"> State the equation of the line asymptotic to the graph (if any)<BR>\n" );
document.write( "y=(1/4)^x-3. Could you help me with this please? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #197952 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=197952\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It is not possible to know whether your equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F4%29%5E%28x-3%29 ALIGN=MIDDLE  ALT=\"y+=+%281%2F4%29%5E%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F4%29%5Ex-3 ALIGN=MIDDLE  ALT=\"y+=+%281%2F4%29%5Ex-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Please use parentheses generously to make your problem clear. The first equation should be typed in as<BR>\n" );
document.write( "y = (1/4)^(x-3)<br><BR>\n" );
document.write( "I will answer the question for both equations. The key to both solutions is to understand what values a positive number raised to a power can be. Your equations both have a positive number, 1/4, raised to some power. No matter what exponent you put on 1/4, the result will NEVER be:<ul><li>Zero. (Remember <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%5E0+=+1 ALIGN=MIDDLE  ALT=\"%281%2F4%29%5E0+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > not zero!)</li><li>Negative. (Remember 1/4 to a negative power is not a negative number. Negative exponents just mean reciprocals. And any reciprocal of 1/4 is still positive.)</li></ul><BR>\n" );
document.write( "While 1/4 to some power can never be zero, it can, however, be an extremely small positive fraction (i.e. a very tiny fraction just above zero). 1/4 to very large positive powers will be very small fractions near zero. The larger the exponent, the closer we get to zero. This is how an asymptote works.<br><BR>\n" );
document.write( "So for<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F4%29%5E%28x-3%29 ALIGN=MIDDLE  ALT=\"y+=+%281%2F4%29%5E%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where y equals a power of 1/4, y = 0 is a horizontal asymptote.<BR>\n" );
document.write( "and for<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F4%29%5Ex-3 ALIGN=MIDDLE  ALT=\"y+=+%281%2F4%29%5Ex-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where y equals a power of 1/4 minus 3, then y = 0-3 = -3 is a horizontal asymptote. </SPAN>\n" );
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