document.write( "Question 66204: the graph of y=f(x). graph each of the following
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\n" ); document.write( "y=f(x+1)+1 \n" ); document.write( "

Algebra.Com's Answer #46929 by Edwin McCravy(20055) $\"\"$ $\"About$

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\r\n" );
document.write( "the graph of y=f(x). graph each of the following\r\n" );
document.write( "y=absolutevalue(f(x))\r\n" );
document.write( "y=-f(x)\r\n" );
document.write( "y=f(-x)\r\n" );
document.write( "y=f(x+1)+1\r\n" );
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document.write( "You forgot to give the equation for f(x).\r\n" );
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document.write( "Suppose this red graph is the graph of f(x)\r\n" );
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document.write( "Then this green graph is f(-x) \r\n" );
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document.write( "Notice that the green graph f(-x) is the \r\n" );
document.write( "reflection of the red graph in the y-axis.\r\n" );
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document.write( "The rule: replacing x by -x in the right \r\n" );
document.write( "side of the equation for f(x) results in \r\n" );
document.write( "a reflection of the graph into (or across)\r\n" );
document.write( "the y-axis\r\n" );
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document.write( "-----------------------------\r\n" );
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document.write( "y = f(x+1)+1\r\n" );
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document.write( "If the red graph below is of f(x)\r\n" );
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document.write( "Then the green graph below is f(x+1) + 1\r\n" );
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document.write( "Two things were done to f(x).  First x was \r\n" );
document.write( "replaced by (x+1) which moves the graph LEFT \r\n" );
document.write( "by 1 unit.\r\n" );
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document.write( "That is y = f(x+1) would have looked like this:\r\n" );
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document.write( "Rule: Replacing x by x+p moves the graph p \r\n" );
document.write( "unit left.  Replacing x by x-p moves the \r\n" );
document.write( "graph p units right.\r\n" );
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document.write( "Then adding +1 to that raised the green \r\n" );
document.write( "graph 1 unit\r\n" );
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document.write( "Rule: Adding +p to the right side moves the\r\n" );
document.write( "graph p units up. Adding -p to the right\r\n" );
document.write( "side moves the graph p units down.\r\n" );
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document.write( "Edwin

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