document.write( "Question 1158865: given the graph of g, describe how the graph of y=-g(2x)+2 can be obtained from the graph of g by steps of transformation \n" ); document.write( "
Algebra.Com's Answer #781909 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "You start with a graph of\r\n" );
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document.write( "y = g(x)  \r\n" );
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document.write( "As an example I'll use y = |x|\r\n" );
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document.write( "Sometimes you do something to x and sometimes you do something to the whole\r\n" );
document.write( "right side.  When you do something to the whole right side, it does something to\r\n" );
document.write( "the graph LIKE you think it should be, but when you do something to x only, it\r\n" );
document.write( "does just the opposite of what you think it should do.\r\n" );
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document.write( "The first thing is doing something to the whole right side, which is multiplying\r\n" );
document.write( "the whole right side by -1, getting\r\n" );
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document.write( "y = -g(x) \r\n" );
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document.write( "The example is y = -|x|\r\n" );
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document.write( "This reflects the graph across the x-axis so that things above the x-axis go\r\n" );
document.write( "below the x-axis and things below the x-axis go above the x-axis.  That's like\r\n" );
document.write( "you would think it should be, because it's done to the whole right side, not\r\n" );
document.write( "just to x.\r\n" );
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document.write( "The next thing is to replace x by 2x.  This is just doing something to x, giving\r\n" );
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document.write( "y = -g(2x)  \r\n" );
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document.write( "The example is y = -|2x|\r\n" );
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document.write( "Normally you would think that multiplying x by 2 would make the curve twice as\r\n" );
document.write( "wide, but it's doing something to just x, so just the opposite is true!  It\r\n" );
document.write( "makes the curve narrower by one half.\r\n" );
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document.write( "Finally you are going to do something to the whole right side, which is to add 2\r\n" );
document.write( "the whole right side. And it does just what you'd think it would.  It shifts the\r\n" );
document.write( "graph up 2 units like this, like you'd expect. \r\n" );
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document.write( "y = -g(2x)+2\r\n" );
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document.write( "The example is y = -|2x|+2\r\n" );
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document.write( "Do something to the whole right side of the equation, it does just what you'd\r\n" );
document.write( "think it does.\r\n" );
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document.write( "Do something to just x, it does the EXACT OPPOSITE of what you'd think it should\r\n" );
document.write( "do.\r\n" );
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document.write( "If you were to replace x by x-3 (Subtract 3 from x) it would moves the curve\r\n" );
document.write( "right 3 units. You would think it would move it left, but when you do something\r\n" );
document.write( "to x only, it does the opposite from what you'd expect.  \r\n" );
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document.write( "If you replace x by x+3 (Add 3 to x) it moves the curve left 3 units.  You would\r\n" );
document.write( "think it would move it right, but when you do something to x, it does the\r\n" );
document.write( "opposite from what you'd expect. \r\n" );
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document.write( "Edwin
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