document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1787>Question 1787</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sketch the graph of each function. state the domain and range, and whether the function is increasing or decreasing. identify any aysmptotes.<BR>\n" );
document.write( "f(x)=2^x-3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #632 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=632\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i am assuming the equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%5E%28x-3%29 ALIGN=MIDDLE  ALT=\"y+=+2%5E%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and not <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282%5Ex%29-3 ALIGN=MIDDLE  ALT=\"y+=+%282%5Ex%29-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, it is a log graph...you should learn how a log or exponential graph looks.\r<BR>\n" );
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document.write( "Always look for \"obvious\" points on any sketching...usually where x=0 and where y=0, although in exponentials, it is better to find where y=1 usually.\r<BR>\n" );
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document.write( "so, if x=0, then y=1/8.<BR>\n" );
document.write( "if y=1, then x=3.\r<BR>\n" );
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document.write( "the curve never quite reaches the x-axis on the -ve x-side...put in a large -ve x-value and you will see this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C+200%2C+-3%2C+5%2C+-1%2C+6%2C+2%5E%28x-3%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C+200%2C+-3%2C+5%2C+-1%2C+6%2C+2%5E%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "the graph is increasing and has an asymptote at x=0, as the function \r<BR>\n" );
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document.write( "sorry, i missed off the domain and range...\r<BR>\n" );
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document.write( "domain is xeR (ie all real values of x)<BR>\n" );
document.write( "range is yeR, y>0 (ie all real values greater than 0, since no -ve y values are possible...nor is zero).\r<BR>\n" );
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document.write( "cheers<BR>\n" );
document.write( "Jon. </SPAN>\n" );
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