document.write( "Question 470844: list the transformation required to obtain the graph of
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Algebra.Com's Answer #322974 by Edwin McCravy(20060)\"\" \"About 
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y= π-3sin^-1 (1-4x) from y=sin^-1 x
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document.write( "To find out the operations, we must first \"route out\" the path\r\n" );
document.write( "from  y = sin-1(x) to y = p - 3sin-1(1 - 4x)\r\n" );
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document.write( "To find the \"route\", we change the expression in\r\n" );
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document.write( "y = f(x) to  y = A*f[B(x+C)] + D\r\n" );
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document.write( "First we change the expression in parentheses to the form B(x+C)\r\n" );
document.write( "in parentheses:\r\n" );
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document.write( "     1 - 4x\r\n" );
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document.write( "Write it in descending order\r\n" );
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document.write( "    -4x + 1\r\n" );
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document.write( "Factor out the coefficient of x\r\n" );
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document.write( "   -4(x - \"1%2F4\")\r\n" );
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document.write( "So to build that expression from x\r\n" );
document.write( "one operation at a time of replacing x:\r\n" );
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document.write( "We go from x to -x to -4x to -4(x - \"1%2F4\")\r\n" );
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document.write( "which means we go from the graph of\r\n" );
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document.write( "y = sin-1(x) \r\n" );
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document.write( "to the graph of\r\n" );
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document.write( "y = sin-1(-x)\r\n" );
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document.write( "to the graph of\r\n" );
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document.write( "y = sin-1(-4x)}}})\r\n" );
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document.write( "to the graph of\r\n" );
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document.write( "y = sin-1[-4(x - \"1%2F4\")]\r\n" );
document.write( "\r\n" );
document.write( "to the graph of\r\n" );
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document.write( "y = -sin-1[-4(x - \"1%2F4\")]\r\n" );
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document.write( "to the graph of\r\n" );
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document.write( "y = -3sin-1[-4(x - \"1%2F4\")]\r\n" );
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document.write( "to the graph of\r\n" );
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document.write( "y = -3sin-1[-4(x - \"1%2F4\")] + p\r\n" );
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document.write( "The first operation in going from the graph of\r\n" );
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document.write( "y = sin-1(x) \r\n" );
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document.write( "which is this\r\n" );
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document.write( "\"graph%28200%2C650%2C-2%2C2%2C+-5%2C8%2C+asin%28x%29%29\"\r\n" );
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document.write( "to the graph of \r\n" );
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document.write( "y = sin-1(-x)\r\n" );
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document.write( "involves replacing x by -x which is a \r\n" );
document.write( "reflection across (or into) the y-axis:\r\n" );
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document.write( "\"graph%28200%2C650%2C-2%2C2%2C+-5%2C8%2C+asin%28-x%29%29\"\r\n" );
document.write( "   \r\n" );
document.write( "Next we go from that graph to the graph of\r\n" );
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document.write( "y = sin-1(-4x)\r\n" );
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document.write( "That involves replacing x by 4x which is a \r\n" );
document.write( "horizontal shrinking of the graph by a factor of \"1%2F4\":\r\n" );
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document.write( "\"graph%28200%2C650%2C-2%2C2%2C+-5%2C8%2C+asin%28-4x%29%29\"\r\n" );
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document.write( "Next we go from that graph to the graph of\r\n" );
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document.write( "y = sin-1[-4(x - \"1%2F4\")]\r\n" );
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document.write( "That involves replacing x by x - \"1%2F4\"\r\n" );
document.write( "which is a right shift of \"1%2F4\" a unit:\r\n" );
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document.write( "\"graph%28200%2C650%2C-2%2C2%2C+-5%2C8%2C+asin%281-4x%29%29\"\r\n" );
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document.write( "Now we go from that graph to the graph of\r\n" );
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document.write( "y = -sin-1[-4(x - \"1%2F4\")]\r\n" );
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document.write( "which involves multiplying the whole right side by -1,\r\n" );
document.write( "which reflects the graph across (or into) the\r\n" );
document.write( "x-axis:\r\n" );
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document.write( "\"graph%28200%2C650%2C-2%2C2%2C+-5%2C8%2C+-asin%281-4x%29%29\"\r\n" );
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document.write( "Now we go from that graph to the graph of\r\n" );
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document.write( "y = -3sin-1[-4(x - \"1%2F4\")]\r\n" );
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document.write( "which involves multiplying the whole right side by 3,\r\n" );
document.write( "which stretches the graph by a factor of 3\r\n" );
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document.write( "\"graph%28200%2C650%2C-2%2C2%2C+-5%2C8%2C+-3asin%281-4x%29%29\"\r\n" );
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document.write( "Finally we go from that graph to the graph of \r\n" );
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document.write( "y = -3sin-1[-4(x - \"1%2F4\")] + p\r\n" );
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document.write( "which involves adding p to the right side,\r\n" );
document.write( "which shifts the graph vertically p units upward:\r\n" );
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document.write( "\"graph%28200%2C650%2C-2%2C2%2C+-5%2C8%2C+pi-3asin%281-4x%29%29\"\r\n" );
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document.write( "Edwin
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