document.write( "Question 1086373: 25.
\n" ); document.write( "State the various transformations applied to the base function ƒ(x) = |x| to obtain a graph of the function g(x) = −|x| + 2.
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\n" ); document.write( "1. A reflection about the y-axis and a vertical shift upward of 2 units.
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\n" ); document.write( "2. A reflection about the x-axis and a vertical shift upward of 2 units.
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\n" ); document.write( "3. A reflection about the y-axis and a vertical shift downward of 2 units.
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\n" ); document.write( "4. A reflection about the x-axis and a vertical shift downward of 2 units.\r
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Algebra.Com's Answer #700567 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "First lets get the proper path to start with |x| and end up with\r\n" );
document.write( "-|x|+2\r\n" );
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document.write( "Step 1.  |x|      <--an upward v-shaped graph with vertex (0,0) going through\r\n" );
document.write( "                     (1,1) and (-1,1)  \r\n" );
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document.write( "Step 2. -|x|      <--multiply by -1, which reflects the graph\r\n" );
document.write( "                     across the x-axis. \r\n" );
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document.write( "Step 3. -|x| + 2  <--add +2, which shifts the graph upward 2 units.\r\n" );
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document.write( "(Always do addition to the right side or subtraction from the right\r\n" );
document.write( "side last.)\r\n" );
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document.write( "Here they are:\r\n" );
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document.write( "Step 1. f(x) = |x|      <--an upward v-shaped graph with vertex (0,0) going through\r\n" );
document.write( "                     (1,0) and (-1,0). That's the red graph below:  \r\n" );
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document.write( "                      \r\n" );
document.write( "Step 2. h(x) = -|x|     <--multiply right side by -1, which reflects the graph\r\n" );
document.write( "                        across the y-axis.  That's the green graph below:  \r\n" );
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document.write( "Step 3. g(x) = -|x| + 2  <--add +2, which shifts the graph upward 2 units. That's\r\n" );
document.write( "                  the black graph below.\r\n" );
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document.write( "Edwin
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