document.write( "Question 90207: HELP PLEASE!!!!! THANK YOU
\n" ); document.write( "I need to take the original functions and define f(x). Then find the new equations by applying the shifts and simplify?!?!?!?!?!?!?\r
\n" ); document.write( "\n" ); document.write( "1. y=x^2-2 shift down 3 and left 4
\n" ); document.write( "2. y=2x=3 shift left 5
\n" ); document.write( "3. y=4x-2 shift down 3 and right 2
\n" ); document.write( "4. y=-1/2x^2 shift left 4 and widen by 2\r
\n" ); document.write( "\n" ); document.write( "Thank you for your help
\n" ); document.write( "llo
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Algebra.Com's Answer #65468 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "HELP PLEASE!!!!! THANK YOU\r\n" );
document.write( "I need to take the original functions and define f(x). \r\n" );
document.write( "Then find the new equations by applying the shifts and simplify?!?!?!?!?!?!? \r\n" );
document.write( "1. \"y=x%5E2-2\" shift down 3 and left 4\r\n" );
document.write( "2. \"y=2x=3\" shift left 5\r\n" );
document.write( "3. \"y=4x-2\" shift down 3 and right 2\r\n" );
document.write( "4. \"y=-%281%2F2%29x%5E2\" shift left 4 and widen by 2 \r\n" );
document.write( "Thank you for your help\r\n" );
document.write( "llo\r\n" );
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document.write( "Rules:\r\n" );
document.write( "1. To shift UP N units, ADD +N TO THE RIGHT SIDE.\r\n" );
document.write( "2. TO shift DOWN N units, ADD -N TO THE RIGHT SIDE.\r\n" );
document.write( "3. To shift RIGHT N units, REPLACE x by (x - N) \r\n" );
document.write( "4. To shift LEFT N units, REPLACE x by (x + N)\r\n" );
document.write( "5. To STRETCH by a factor of N > 1, MULTIPLY the RIGHT SIDE by N.\r\n" );
document.write( "6. To SHRINK by a factor of N < 1, MULTIPLY the RIGHT SIDE by N\r\n" );
document.write( "7. To SHRINK by a factor of N > 1, MULTIPLY the RIGHT SIDE by 1/N\r\n" );
document.write( "7. To WIDEN by a factor of N > 1, REPLACE x by x/N\r\n" );
document.write( "8. To NARROW by a factor of N < 1, REPLACE x by Nx\r\n" );
document.write( "9. To REFLECT across the x-axis, MULTIPLY the RIGHT SIDE by -1\r\n" );
document.write( "10. To REFLECT across the y-axis, REPLACE x by -x\r\n" );
document.write( "11. TO REFLECT across the origin, REFLECT in the y-axis and then REFLECT in the x-axis.\r\n" );
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document.write( "1. \"y+=+x%5E2+-+2\" shift down 3 and left 4\r\n" );
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document.write( "Shifting down 3 requires adding -3 to the right side, so first we have\r\n" );
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document.write( "\"y+=+x%5E2+-+2+-+3\"\r\n" );
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document.write( "Simplifying,\r\n" );
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document.write( "\"y+=+x%5E2+-+5\"\r\n" );
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document.write( "Shifting left 4 requires replacing x by (x + 4)  so\r\n" );
document.write( "now we have:\r\n" );
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document.write( "\"y+=+%28x+%2B+4%29%5E2+-+5\"\r\n" );
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document.write( "\"y+=+x%B2+%2B+8x+%2B+16+-+5\"\r\n" );
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document.write( "\"y+=+x%B2+%2B+8x+%2B+11\"\r\n" );
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document.write( "Label it \"f%28x%29\"\r\n" );
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document.write( "\"f%28x%29+=+x%B2+%2B+8x+%2B+11\"\r\n" );
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document.write( "-------------------------------\r\n" );
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document.write( "2. y=2x=3 shift left 5\r\n" );
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document.write( "You botched that equation, that second = should either be a + or a -,\r\n" );
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document.write( "Either way, to shift left 5, replace \"x\" by \"%28x+%2B+5%29\"\r\n" );
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document.write( "If it was supposed to be \"y+=+2x+%2B+3\", then when we shift that left 5 we get\r\n" );
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document.write( "\"y+=+2%28x+%2B+5%29+%2B+3\"\r\n" );
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document.write( "\"y+=+2x+%2B+10+%2B+3\"\r\n" );
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document.write( "\"y+=+2x+%2B+13\"\r\n" );
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document.write( "If it was supposed to be \"y+=+2x+-+3\", then when we shift that left 5 we get\r\n" );
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document.write( "\"y+=+2%28x+%2B+5%29+-+3\"\r\n" );
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document.write( "\"y+=+2x+%2B+10+-+3\"\r\n" );
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document.write( "\"y+=+2x+%2B+7\"\r\n" );
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document.write( "Label it \"f%28x%29\"\r\n" );
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document.write( "\"f%28x%29=3x%2B7\"\r\n" );
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document.write( "----------------------------------------------\r\n" );
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document.write( "3. \"y+=+4x+-+2\" shift down 3 and right 2\r\n" );
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document.write( "To shift down 3 we add -3 to the right side:\r\n" );
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document.write( "\"y+=+4x+-+2+-+3\"\r\n" );
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document.write( "\"y+=+4x+-+5\"\r\n" );
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document.write( "To shift right 2 we replace \"x\" by \"%28x+-+2%29\" in the right side\r\n" );
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document.write( "\"y+=+4%28x+-+2%29+-+5\"\r\n" );
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document.write( "\"y+=+4x+-+8+-+5\"\r\n" );
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document.write( "\"y+=+4x+-+13\"\r\n" );
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document.write( "Label it f(x)\r\n" );
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document.write( "\"f%28x%29=4x-15\" \r\n" );
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document.write( "--------------------------------------\r\n" );
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document.write( "4. \"y+=+-%281%2F2%29x%5E2\" shift left 4 and widen by 2\r\n" );
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document.write( "To shift left 4 units we replace \"x\" by \"%28x+%2B+4%29\"\r\n" );
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document.write( "\"y+=+-%281%2F2%29%28x+%2B+4%29%5E2\"\r\n" );
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document.write( "To widen by 2, we replace x by \"%28x%2F2%29\" \r\n" );
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document.write( "\"y+=+-%281%2F2%29%28x%2F2+%2B+4%29%5E2\"\r\n" );
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document.write( "\"y+=+-%281%2F2%29%28x%2F2%2B8%2F2%29%5E2\"\r\n" );
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document.write( "\"y+=+-%281%2F2%29%28%28x%2B8%29%2F2%29%5E2\"\r\n" );
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document.write( "\"y+=+-%281%2F2%29%28%28x%2B8%29%5E2%2F%282%5E2%29%29\"\r\n" );
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document.write( "\"y+=+-%281%2F2%29%28%28x%2B8%29%5E2%2F4%29\"\r\n" );
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document.write( "\"y+=+-%281%2F8%29%28x%2B8%29%5E2\"\r\n" );
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document.write( "\"y+=+-%281%2F8%29%28x%5E2%2B16x%2B64%29\"\r\n" );
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document.write( "\"y+=+-%281%2F8%29x%5E2-2x-8\"\r\n" );
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document.write( "Label it \"f%28x%29\"\r\n" );
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document.write( "\"f%28x%29+=+-%281%2F8%29x%5E2-2x-8\"\r\n" );
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document.write( "Edwin
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