document.write( "Question 85096: I have a question that states: use the graph of f(x)=/x/ to find the graph of f(x)=/x+4/-3. \n" ); document.write( "
Algebra.Com's Answer #61359 by bucky(2189)\"\" \"About 
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The answer to this problem will probably be easier to understand if you can see what the
\n" ); document.write( "two given graphs look like. So let's begin by graphing \"y+=+abs%28x%29\" and \"y+=+abs%28x%2B4%29-3\":
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\n" ); document.write( "\"graph%28300%2C300%2C-10%2C10%2C-5%2C10%2Cabs%28x%29%2Cabs%28x%2B4%29-3%29\"
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\n" ); document.write( "The brown graph is the graph of \"y+=+abs%28x%29\" and the green graph is is the graph of
\n" ); document.write( "\"y+=+abs%28x%2B4%29-3\"
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\n" ); document.write( "Notice that if you take the graph of \"y+=+abs%28x%29\" and move it 4 units to the left and
\n" ); document.write( "then down 3 units, you get the graph of \"y+=+abs%28x%2B4%29-3\". The 4 units to the left comes
\n" ); document.write( "from the x+4 in the absolute value signs. The sign of the 4 is + so you move in the opposite
\n" ); document.write( "direction, that is move in the minus direction 4 units. When you do that you get the graph of
\n" ); document.write( "\"y+=+abs%28x%2B4%29\" which is shown in purple on the graph below:
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\n" ); document.write( "\"graph%28300%2C300%2C-10%2C10%2C-5%2C10%2Cabs%28x%29%2Cabs%28x%2B4%29-3%2Cabs%28x%2B4%29%29\"
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\n" ); document.write( "Then the -3 of the original translation comes into play. It lowers the purple graph by
\n" ); document.write( "3 units so that it sits on top of the green graph.
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\n" ); document.write( "In summary, take the original graph of \"y+=+abs%28x%29\" and shift it to the left 4 units, and
\n" ); document.write( "then shift it down 3 units to get the graph of \"y+=+abs%28x%2B4%29-3\"
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\n" ); document.write( "Hope this helps you to visualize what is happening with the translation.
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