document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159204>Question 159204</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Seeking assistance.\r<BR>\n" );
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document.write( "Describe transformations of the graph of f(x)=e^x. Note horizontal asymptote and y-intercept after the transformation. <BR>\n" );
document.write( "a)g(x) = e^x + 3<BR>\n" );
document.write( "  Graph: vertical shift of 3 units up.<BR>\n" );
document.write( "  Equation for horizontal asymptote: x = 2.72 + 2, 4.72<BR>\n" );
document.write( "  y-intercept: (0,3)\r<BR>\n" );
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document.write( "b)h(x) = -e^x<BR>\n" );
document.write( "  Graph: reflection around y axis<BR>\n" );
document.write( "  Equation: -1e^x = 0, e^x = 1<BR>\n" );
document.write( "  y-intercept: (1,0)\r<BR>\n" );
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document.write( "The above is what has been attempted. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117392 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=117392\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first one to get you started\r<BR>\n" );
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document.write( "a)\r<BR>\n" );
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document.write( "a)g(x) = e^x + 3\r<BR>\n" );
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document.write( "Graph: vertical shift of 3 units up. Correct.\r<BR>\n" );
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document.write( "Equation for horizontal asymptote:  When \"x\" is a very large negative number, then <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;\" > becomes really small (and eventually approaches zero). \r<BR>\n" );
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document.write( "So what's left over is the term \"3\". So the horizontal asymptote is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3 ALIGN=MIDDLE  ALT=\"y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "y-intercept: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=e%5Ex%2B3 ALIGN=MIDDLE  ALT=\"g%28x%29=e%5Ex%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%280%29=e%5E0%2B3 ALIGN=MIDDLE  ALT=\"g%280%29=e%5E0%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%280%29=1%2B3 ALIGN=MIDDLE  ALT=\"g%280%29=1%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Raise \"e\" to the zeroth power to get 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%280%29=4 ALIGN=MIDDLE  ALT=\"g%280%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "So when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (g(x) and y are interchangeable) \r<BR>\n" );
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document.write( "So the y-intercept is (0,4)\r<BR>\n" );
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document.write( "Here's a graph to verify the answer.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2Cexp%28x%29%2B3%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=e%5Ex%2B3 ALIGN=MIDDLE  ALT=\"g%28x%29=e%5Ex%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "Use the techniques used above to solve this problem. </SPAN>\n" );
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