document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195058>Question 1195058</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the domain, range, equation of the horizontal asymptote and construct the graph of the following exponential function: f(x) =6^3-x  - 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #827396 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=827396\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The function you show is not an exponential function:<br><BR>\n" );
document.write( "f(x) = 6^3-x-4 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+6%5E3-x-4 ALIGN=MIDDLE  ALT=\"f%28x%29+=+6%5E3-x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "If you are working on a problem like this, your math knowledge should be enough to know that proper use of parentheses is important.<br><BR>\n" );
document.write( "Since you said the function is exponential, undoubtedly the function you intended to show is this:<br><BR>\n" );
document.write( "f(x) = 6^(3-x)-4 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+6%5E%283-x%29-4 ALIGN=MIDDLE  ALT=\"f%28x%29+=+6%5E%283-x%29-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "domain: all real numbers.  There is no restriction on the input value in any exponential equation.<br><BR>\n" );
document.write( "range and horizontal asymptote: The range is (-4,infinity).  Without the \"-4\", the exponential function value is always positive but gets as close to 0 as you want.  So with the \"-4\" the horizontal asymptote is y=-4.<br><BR>\n" );
document.write( "a graph, showing the horizontal asymptote:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-1%2C6%2C-10%2C10%2C6%5E%283-x%29-4%2C-4%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-1%2C6%2C-10%2C10%2C6%5E%283-x%29-4%2C-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );