document.write( "Question 1046530: A function f(x) contains points A, B, C, and D
\n" ); document.write( "A(-2,0)
\n" ); document.write( "B(0,2)
\n" ); document.write( "C(3,-1)
\n" ); document.write( "D(4,4)\r
\n" ); document.write( "\n" ); document.write( "The function is transformed to create g(x)
\n" ); document.write( "Such that g(x) = f (1/2 x) - 4.
\n" ); document.write( "Complete the table to show coordinates of points A', B', C', and D'\r
\n" ); document.write( "\n" ); document.write( "A'
\n" ); document.write( "B'
\n" ); document.write( "C'
\n" ); document.write( "D'
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Algebra.Com's Answer #662031 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Here are the 5 rules for what happens to each point of a \r\n" );
document.write( "graph when x is replaced by something in the right side \r\n" );
document.write( "of the equation. Assume in all cases that k is a positive \r\n" );
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document.write( "1. Replacing x by -x\r\n" );
document.write( "   [Reflects graph across the y-axis]\r\n" );
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document.write( "2. Replacing x by (x+k)\r\n" );
document.write( "   [Shifts graph k units left] \r\n" );
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document.write( "3. Replacing x by (x-k).\r\n" );
document.write( "   [Shifts graph k units right]    \r\n" );
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document.write( "4. Replacing x by kx, where k > 1\r\n" );
document.write( "   [Shrinks graph horizontally by a factor of 1/k. \r\n" );
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document.write( "5. Replacing x by x, where k > 1\r\n" );
document.write( "   [Stretches graph horizontally by a factor of k.\r\n" );
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document.write( "Here are the 5 rules for what happens to a graph when \r\n" );
document.write( "something is done to the right side of the equation:\r\n" );
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document.write( " 6. Multiplying the right side of the equation by -1\r\n" );
document.write( "    [Reflects graph across the x-axis]\r\n" );
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document.write( " 7. Adding k to the right side of the equation\r\n" );
document.write( "    [Shifts graph k units upward]\r\n" );
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document.write( " 8. Subtracting k from the right side of an equation\r\n" );
document.write( "    [Shifts graph k units downward]\r\n" );
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document.write( " 9. Multiplying the right side of the equation by k, where k > 1\r\n" );
document.write( "    [Stretches graph vertically by a factor of k]\r\n" );
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document.write( "10. Multiplying the right side of the equation by k, where 0 < k < 1\r\n" );
document.write( "    [Shrinks graph vertically by a factor of 1/k]\r\n" );
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document.write( "-----------------------------\r\n" );
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document.write( "We are to find .\r\n" );
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document.write( "Using rule 5, replacing x in the right side of the equation of f(x)\r\n" );
document.write( "by  would stretch horizontally by a factor of 2,\r\n" );
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document.write( "So A(-2,0) would stretch horizontally to (-2*2,0) = (-4,0),\r\n" );
document.write( "   B(0,2) would stretch horizontally to (0*2,2) = (0,2)\r\n" );
document.write( "   C(3,-1) would stretch horizontally to (3*2,-1) = (6,-1)\r\n" );
document.write( "   D(4,4) would stretch horizontally to (4*2,0) = (8,0)\r\n" );
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document.write( "Then by rule 8, subtracting 4 from the right side of \r\n" );
document.write( "would shift vertically DOWNWARD by 4 units\r\n" );
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document.write( "So (-4,0) would shift vertically downward to A'(-4,0-4) = A'(-4,-4)\r\n" );
document.write( "   (0,2) would shift vertically downward to B'(0,2-4) = B'(0,-2)\r\n" );
document.write( "   (6,-1) would shift vertically downward to C'(6,-1-4) = C'(6,-5)\r\n" );
document.write( "   (8,0) would shift vertically downward to D'(8,0-4) = D'(8,-4)\r\n" );
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document.write( "Edwin

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