document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159561>Question 1159561</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the curve described by the equation below,<BR>\n" );
document.write( "y = e^2x + 3.<BR>\n" );
document.write( "a) Sketch a rough graph of this curve. Clearly label the x and y axis,<BR>\n" );
document.write( "label the points where the curve crosses any axis. Draw a dashed line on<BR>\n" );
document.write( "the graph to indicate any asymptotes, find the equation of any asymptotes\r<BR>\n" );
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document.write( "b) Find the equation of the straight line stated below,<BR>\n" );
document.write( "y = mx + c,<BR>\n" );
document.write( "that is a tangent to the curve at the point x = 0. State the value of the<BR>\n" );
document.write( "gradient m and the y intercept c.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #782607 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=782607\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Do you mean:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ e^{2x}\ +\ 3\">\r<BR>\n" );
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document.write( "in which case you should have written y = e^(2x) + 3\r<BR>\n" );
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document.write( "or did you mean:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ e^{2x\,+\,3}\">\r<BR>\n" );
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document.write( "in which case you should have written y = e^(2x + 3)\r<BR>\n" );
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document.write( "I rejected the third possible interpretation of your utterly ambiguous post which was:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ e^{2}x\ +\ 3\">\r<BR>\n" );
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document.write( "because you called the graph a curve and this interpretation would result in a straight line with a slope of e squared.\r<BR>\n" );
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document.write( "So your first lesson is to learn to use parentheses appropriately so that we don't have to guess what you mean.  For more information on rendering mathematical expressions in plain text see <a  rel=nofollow HREF=\"https://www.purplemath.com/modules/mathtext.htm\">Purple Math: Formatting Math as Text</a>.  Note that this link takes you to the first of four pages on the subject.  I recommend that you read all of them.\r<BR>\n" );
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document.write( "Re-post when you figure out how to communicate with us effectively.<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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