document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=47734>Question 47734</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534373526/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Graph the function, not by plotting points, but by starting from the graph of y = e^x.  State the domain, range, and asymptote.\r<BR>\n" );
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document.write( "y = 1- e^x\r<BR>\n" );
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document.write( "I tried graphing these on the computer but it won't take these exponents so I'm at a loss although I know that there is some shifting involved with the first constant. \r<BR>\n" );
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document.write( "Thank you so very much for this help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #31632 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=31632\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sketching graphs is one of the most important skills you can have in your arsenal in maths. Forget graphical calculators..they are rubbish in my honest opinion.\r<BR>\n" );
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document.write( "start with LEARNING the shape of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=e%5Ex ALIGN=MIDDLE  ALT=\"y=e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >. I cannot draw it here, but look in your books. Learn its shape and the fact that it has no y-values and that when x=0, then y=1.\r<BR>\n" );
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document.write( "Right, what about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-e%5Ex ALIGN=MIDDLE  ALT=\"y=-e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Adding a negative sign has the action of flipping the whole curve upside down, as if mirrored in the x-axis.\r<BR>\n" );
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document.write( "So we now have the same shaped curve but it exists completely under the x-axis now and goes through (0,-1).\r<BR>\n" );
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document.write( "Now, finally we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1-e%5Ex ALIGN=MIDDLE  ALT=\"y=1-e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > which you can think of as y=1 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-e%5Ex ALIGN=MIDDLE  ALT=\"-e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we have the -ve curve and we add a value of 1 to each point. This has the effect of moving the whole curve up by 1 unit, so the shape is unaltered and whereas we had the curve skimming along the x-axis for negative values of x, now we have the curve skimming along x=1 and then it moves down through (0,0) instead of (0,-1).\r<BR>\n" );
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document.write( "Hope this makes sense.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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