document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=973265>Question 973265</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the reflection of the graph of y=2^x across the y axis?<BR>\n" );
document.write( "Y=-2^x<BR>\n" );
document.write( "Y=.5(2^x)<BR>\n" );
document.write( "Y=(1/2)^x<BR>\n" );
document.write( "Y=5(2^x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #595507 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=595507\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe it will be y = (1/2)^x\r<BR>\n" );
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document.write( "it was derived as follows:\r<BR>\n" );
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document.write( "you know that 2^2 = 4\r<BR>\n" );
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document.write( "you want some value of b^(-2) to be also equal to 4\r<BR>\n" );
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document.write( "you start with b^(-2) = 4\r<BR>\n" );
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document.write( "take the log of both sides of the equation to get:\r<BR>\n" );
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document.write( "log(b^(-2)) = log(4)\r<BR>\n" );
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document.write( "since log(b^a) = a*log(b), that equation becomes:\r<BR>\n" );
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document.write( "-2*log(b) = log(4)\r<BR>\n" );
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document.write( "divide both sides of that equation by -2 to get:\r<BR>\n" );
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document.write( "log(b) = log(4)/(-2)\r<BR>\n" );
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document.write( "evaluate that equation to get:\r<BR>\n" );
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document.write( "log(b) = .6020599913/(-2) = -.3010299957\r<BR>\n" );
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document.write( "by the basic law of logarithms that says y = log(x) if and only if 10^y = x, you get:\r<BR>\n" );
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document.write( "log(b) = -.3010299957 if and only if 10^-.301029997 = b\r<BR>\n" );
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document.write( "solve for b to get b = .5 which is equal to 1/2.\r<BR>\n" );
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document.write( "you wound up with b^(-2) = 4 if and only if b = 1/2.\r<BR>\n" );
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document.write( "your solution is therefore that y = (1/2)^x.\r<BR>\n" );
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document.write( "here's the graph of y = 2^x and y = (1/2)^x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/060102.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you can see that these two equations are reflections of each other about the  y-axis.\r<BR>\n" );
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document.write( "this may have been the hard way to derive it.\r<BR>\n" );
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document.write( "usually you just replace x with -x and you should get the equivalent equation that's a reflection of the original equation about the y-axis.\r<BR>\n" );
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document.write( "start with y = 2^x\r<BR>\n" );
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document.write( "replace x with (-x) to get:\r<BR>\n" );
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document.write( "y = 2^(-x)\r<BR>\n" );
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document.write( "that's the same as y = 1 / 2^x\r<BR>\n" );
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document.write( "since 1 to any power is equal to 1, that equivalent to y = 1^x / 2^x which is the same as y = (1/2)^x.\r<BR>\n" );
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document.write( "the solution was derived in two different ways.\r<BR>\n" );
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document.write( "i think the second way was easier.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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