document.write( "Question 1090782: can someone please help me with this As soon as possible?\r
\n" ); document.write( "\n" ); document.write( "Use transformations to sketch the function y=-3(2^x+6)-1. State the domain and range \n" ); document.write( "

Algebra.Com's Answer #705230 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "I'll assume you meant  and not ,\r\n" );
document.write( "which is what you wrote meant because you didn't put the \r\n" );
document.write( "exponent in parentheses and so the +6 didn't get included \r\n" );
document.write( "in the exponent when you don't put parentheses to include it.\r\n" );
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document.write( "Start with .  I'll mark the point (1,2)\r\n" );
document.write( "and show what happens to that point:\r\n" );
document.write( "Domain (-oo,oo), Range (0,oo)\r\n" );
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document.write( "Next replace x by x+6 which shifts the graph 6 units left.\r\n" );
document.write( "This is the graph is of .\r\n" );
document.write( "Notice that the point (1,2) shifts horizontally 6 units left \r\n" );
document.write( "to (-5,2): \r\n" );
document.write( "Domain (-oo,oo), Range (0,oo)\r\n" );
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document.write( "Next multiply by -1, which reflects it into (across) the x-axis\r\n" );
document.write( "This is the graph of \r\n" );
document.write( "Notice that the point (-5,2) reflects across the x-axis to (-5,-2): \r\n" );
document.write( "Domain (-oo,oo), Range (-oo,0)\r\n" );
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document.write( "Next multiply by 3 which stretches it vertically by a factor of 3.  \r\n" );
document.write( "This is as if the graph were on a rubber sheet and we stretched the \r\n" );
document.write( "rubber sheet three times vertically.\r\n" );
document.write( "This is the graph of \r\n" );
document.write( "Notice that the point (-5,-2) stretches vertically by a factor of\r\n" );
document.write( "3 to (-5,-6): \r\n" );
document.write( "Domain (-oo,oo), Range (-oo,0)\r\n" );
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document.write( "Finally we add -1 which shifts it down 1 unit.\r\n" );
document.write( "Notice that the point (-5,-6) shifts vertically down to (-5,-7) \r\n" );
document.write( "This is the final graph:\r\n" );
document.write( "Domain (-oo,oo), Range (-oo,-1).  Notice that the horizontal\r\n" );
document.write( "asymptote did not move until now. It moved from the x-axis (y=0)\r\n" );
document.write( "to the green dotted line y=-1:\r\n" );
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document.write( "Edwin

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