document.write( "Question 887887: state the transforamtion necessary to transform
\n" ); document.write( "f(x)=1/2(2^3x)-4 to g(x)=8^x
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Algebra.Com's Answer #536907 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"%22f%28x%29%22\"\"%22%22=%22%22\"\"expr%281%2F2%29%282%5E%283x%29%29-4\" to \"%22g%28x%29%22\"\"%22%22=%22%22\"\"8%5Ex\"\r\n" );
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document.write( "The graph of \"%22f%28x%29%22\" is the red graph below\r\n" );
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document.write( "\"graph%28640%2F3%2C400%2C-5%2C3%2C-5%2C10%2C+%281%2F2%29%282%5E%283x%29%29-4%29\"\r\n" );
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document.write( "Write that as:\r\n" );
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document.write( "\"%22f%28x%29%22\"\"%22%22=%22%22\"\"expr%281%2F2%29%28%282%5E3%29%5Ex%29-4\"\r\n" );
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document.write( "Then as\r\n" );
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document.write( "\"%22f%28x%29%22\"\"%22%22=%22%22\"\"expr%281%2F2%29%288%5Ex%29-4\"\r\n" );
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document.write( "Then we form h(x) by adding 4 to the right side\r\n" );
document.write( "which shifts the graph 4 units up\r\n" );
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document.write( "\"%22h%28x%29%22\"\"%22%22=%22%22\"\"expr%281%2F2%29%288%5Ex%29-4%2Bred%284%29\"\r\n" );
document.write( "\"%22h%28x%29%22\"\"%22%22=%22%22\"\"expr%281%2F2%29%288%5Ex%29\"\r\n" );
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document.write( "The graph of h(x) is the green graph below\r\n" );
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document.write( "Finally we form g(x) by multiplying the right side of h(x) by 2.\r\n" );
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document.write( "\"%22g%28x%29%22\"\"%22%22=%22%22\"\"red%282%29%2Aexpr%281%2F2%29%288%5Ex%29\"\r\n" );
document.write( "\"%22g%28x%29%22\"\"%22%22=%22%22\"\"8%5Ex\"\r\n" );
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document.write( "which stretches the green graph by a factor of 2.  That's the same as \r\n" );
document.write( "if the graph of h(x) were on a rubber sheet and then we stretched the \r\n" );
document.write( "rubber sheet to double its size.\r\n" );
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document.write( "So the final graph of \"%22g%28x%29%22\"\"%22%22=%22%22\"\"8%5Ex\" is the blue graph\r\n" );
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document.write( "So the transformation is first to h(x), by adding 4 to the right side:\r\n" );
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document.write( "h(x) = f(x)+4\r\n" );
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document.write( "then the second transformation is from h(x) to g(x), by multiplying the\r\n" );
document.write( "right side of h(x) by 2, or\r\n" );
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document.write( "g(x) = 2h(x)\r\n" );
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document.write( "then you can substitute f(x)+4 for h(x) and get\r\n" );
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document.write( "g(x) = 2[f(x)+4]\r\n" );
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document.write( "or \r\n" );
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document.write( "g(x) = 2f(x)+8\r\n" );
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document.write( "Edwin
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