document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251578>Question 251578</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help me with these two questions? Thanks\r<BR>\n" );
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document.write( "1. Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation; and evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1.  Use the resulting ordered pairs to plot the graph of each function; y=2^x, x=2^y\r<BR>\n" );
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document.write( "8. Evaluate the exponential function for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph; State the domain and the range of the function.\r<BR>\n" );
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document.write( "f(x) = e^-x -1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183892 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=183892\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first equatioon is y = 2^x\r<BR>\n" );
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document.write( "values of x are:\r<BR>\n" );
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document.write( "-3<BR>\n" );
document.write( "-2<BR>\n" );
document.write( "-1<BR>\n" );
document.write( "0<BR>\n" );
document.write( "1<BR>\n" );
document.write( "2<BR>\n" );
document.write( "3\r<BR>\n" );
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document.write( "when x = -3, 2^x = 2^(-3) = 1/2^3 = 1/8\r<BR>\n" );
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document.write( "when x = -2, 2^x = 2^(-2) = 1/2^2 = 1/4\r<BR>\n" );
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document.write( "when x = -1, 2^x = 2^(-1) = 1/2^1 = 1/2\r<BR>\n" );
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document.write( "when x = 0, 2^x = 2^0 = 1\r<BR>\n" );
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document.write( "when x = 1, 2^x = 2^1 = 2\r<BR>\n" );
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document.write( "when x = 2, 2^x = 2^2 = 4\r<BR>\n" );
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document.write( "when x = 3, 2^x = 2^3 = 8\r<BR>\n" );
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document.write( "graph of the equation looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C5%2C-1%2C10%2C2%5Ex%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C5%2C-1%2C10%2C2%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "---------------------------------------------------------------------------\r<BR>\n" );
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document.write( "x = 2^y if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%29+=+y ALIGN=MIDDLE  ALT=\"log%282%2Cx%29+=+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "this is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%282%2Cx%29 ALIGN=MIDDLE  ALT=\"y+=+log%282%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "values for x are:\r<BR>\n" );
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document.write( ".1<BR>\n" );
document.write( ".4<BR>\n" );
document.write( ".7<BR>\n" );
document.write( "1<BR>\n" );
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document.write( "3<BR>\n" );
document.write( "4\r<BR>\n" );
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document.write( "when x = .1, y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%29 ALIGN=MIDDLE  ALT=\"log%282%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C.1%29 ALIGN=MIDDLE  ALT=\"log%282%2C.1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C.1%29%2Flog%2810%2C2%29+=+-3.321928095 ALIGN=MIDDLE  ALT=\"log%2810%2C.1%29%2Flog%2810%2C2%29+=+-3.321928095\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when x = .4, y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%29 ALIGN=MIDDLE  ALT=\"log%282%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C.4%29 ALIGN=MIDDLE  ALT=\"log%282%2C.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C.4%29%2Flog%2810%2C2%29+=+-1.321928095 ALIGN=MIDDLE  ALT=\"log%2810%2C.4%29%2Flog%2810%2C2%29+=+-1.321928095\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when x = .7, y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%29 ALIGN=MIDDLE  ALT=\"log%282%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C.7%29 ALIGN=MIDDLE  ALT=\"log%282%2C.7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C.7%29%2Flog%2810%2C2%29+=+-.0514573173 ALIGN=MIDDLE  ALT=\"log%2810%2C.7%29%2Flog%2810%2C2%29+=+-.0514573173\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when x = 1, y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%29 ALIGN=MIDDLE  ALT=\"log%282%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C1%29 ALIGN=MIDDLE  ALT=\"log%282%2C1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C1%29%2Flog%2810%2C2%29+=+0 ALIGN=MIDDLE  ALT=\"log%2810%2C1%29%2Flog%2810%2C2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when x = 2, y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%29 ALIGN=MIDDLE  ALT=\"log%282%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C2%29 ALIGN=MIDDLE  ALT=\"log%282%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C2%29%2Flog%2810%2C2%29+=+1 ALIGN=MIDDLE  ALT=\"log%2810%2C2%29%2Flog%2810%2C2%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when x = 3, y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%29 ALIGN=MIDDLE  ALT=\"log%282%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C3%29 ALIGN=MIDDLE  ALT=\"log%282%2C3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C3%29%2Flog%2810%2C2%29+=+1.584962501 ALIGN=MIDDLE  ALT=\"log%2810%2C3%29%2Flog%2810%2C2%29+=+1.584962501\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when x = 4, y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%29 ALIGN=MIDDLE  ALT=\"log%282%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C4%29 ALIGN=MIDDLE  ALT=\"log%282%2C4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C4%29%2Flog%2810%2C2%29+=+2 ALIGN=MIDDLE  ALT=\"log%2810%2C4%29%2Flog%2810%2C2%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "graph of this equation looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-1%2C5%2C-1%2C5%2Clog%282%2Cx%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-1%2C5%2C-1%2C5%2Clog%282%2Cx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "graph of both equations together looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C10%2C-5%2C10%2C2%5Ex%2Clog%282%2Cx%29%2Cx%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C10%2C-5%2C10%2C2%5Ex%2Clog%282%2Cx%29%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since the equation of y = 2^x is the inverse of equation x = 2^y, these equations are symmetric about the line y = x as shown in the graph.\r<BR>\n" );
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document.write( "8. Evaluate the exponential function for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph; State the domain and the range of the function.<BR>\n" );
document.write( "f(x) = e^-x -1\r<BR>\n" );
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document.write( "equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-x%29+-+1 ALIGN=MIDDLE  ALT=\"e%5E%28-x%29+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "values of x are:\r<BR>\n" );
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document.write( "-3,-2,-1,0,1,2,3\r<BR>\n" );
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document.write( "when x = -3, equation becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-%28-3%29%29+-+1 ALIGN=MIDDLE  ALT=\"e%5E%28-%28-3%29%29+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%283%29-1 ALIGN=MIDDLE  ALT=\"e%5E%283%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 19.08553692\r<BR>\n" );
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document.write( "when x = -2, equation becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-%28-2%29%29+-+1 ALIGN=MIDDLE  ALT=\"e%5E%28-%28-2%29%29+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%282%29-1 ALIGN=MIDDLE  ALT=\"e%5E%282%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6.389056099\r<BR>\n" );
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document.write( "when x = -1, equation becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-%28-1%29%29+-+1 ALIGN=MIDDLE  ALT=\"e%5E%28-%28-1%29%29+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%281%29-1 ALIGN=MIDDLE  ALT=\"e%5E%281%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.718281828\r<BR>\n" );
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document.write( "when x = 0, equation becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%280%29+-+1 ALIGN=MIDDLE  ALT=\"e%5E%280%29+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > =  0\r<BR>\n" );
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document.write( "when x = 1, equation becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-1%29 ALIGN=MIDDLE  ALT=\"e%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -.632120559\r<BR>\n" );
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document.write( "when x = 2, equation becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-2%29-1 ALIGN=MIDDLE  ALT=\"e%5E%28-2%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -.864664717\r<BR>\n" );
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document.write( "when x = 3, equation becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-3%29-1 ALIGN=MIDDLE  ALT=\"e%5E%28-3%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -.950212932\r<BR>\n" );
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document.write( "graph of equation looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C15%2C-3%2C25%2Ce%5E%28-x%29-1%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C15%2C-3%2C25%2Ce%5E%28-x%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the domain of the equation is all real values of x.\r<BR>\n" );
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document.write( "the range of the equation is all real values of y > -1\r<BR>\n" );
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document.write( "x will never be less then or equal to -1.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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