document.write( "Question 92907: If P(4,-5) is a point on the graph of function y= f(x),find the corresponding point on the graph of y=2f(x-6). \r
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Algebra.Com's Answer #67597 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "If P(4,-5) is a point on the graph of function y= f(x),find the corresponding\r\n" );
document.write( "point on the graph of y=2f(x-6). \r\n" );
document.write( "I understand that where ever I see an x, I'm supposed to substitute the\r\n" );
document.write( "function. I am confused in how to deal with the Point(4, -5)\r\n" );
document.write( "Thanks for your consideration.\r\n" );
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document.write( "The object is to figure out what things have been done to f(x) in order to get\r\n" );
document.write( "2f(x-6)\r\n" );
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document.write( "Two things have been done.  \r\n" );
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document.write( "1.  First f(x) has been multiplied by 2 to give 2f(x). That stretches all the\r\n" );
document.write( "points above the x-axis twice as high, and all points below the x-axis twice as\r\n" );
document.write( "low.\r\n" );
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document.write( "2.  Then after doing that, x has been replaced by x-6 in 2f(x), to get 2f(x-6).\r\n" );
document.write( "That shifts all points 6 units right.\r\n" );
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document.write( "Now let's see what has been done to the point (4,-5)\r\n" );
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document.write( "Step 1. has stretched the point (4,-5), which is below the x-axis, twice as low\r\n" );
document.write( "below the x-axis as it is. That is to say, (4,-5) has been stretched down to\r\n" );
document.write( "the point (4,-10) by step 1.\r\n" );
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document.write( "Then Step 2. has shifted the point (4,-10) right by 6 units to the point\r\n" );
document.write( "(10,-10)\r\n" );
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document.write( "So that's the answer (10,-10) \r\n" );
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document.write( "Notice that we could have reversed 1 and 2 above.\r\n" );
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document.write( "Let's swap the two things that have been done above.  \r\n" );
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document.write( "1. x has been replaced by x-6 in f(x), to get f(x-6). That shifts all points 6\r\n" );
document.write( "units right.  \r\n" );
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document.write( "2.  Then after doing that, f(x-6) has been multiplied by 2 to give 2f(x-6).\r\n" );
document.write( "That stretches all the points above the x-axis twice as high, and all points\r\n" );
document.write( "below the x-axis twice as low.\r\n" );
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document.write( "Now let's see what has been done to the point (4,-5)\r\n" );
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document.write( "Step 1.  has shifted the point (4,-5) right by 6 units to the point\r\n" );
document.write( " (10,-5)\r\n" );
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document.write( "Then Step 2 has stretched the point (10,-5), which is below the x-axis, twice\r\n" );
document.write( "as low below the x-axis as it is. That is to say, (10,-5) has been stretched\r\n" );
document.write( "down to the point (10,-10) by step 1.\r\n" );
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document.write( "So either way you get (10,-10) as the point on y = 2f(x-6) corresponding to the\r\n" );
document.write( "point (4,-5) on f(x).\r\n" );
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document.write( "Edwin
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