document.write( "Question 388660: Graph f(x) = sin (x − 2π) − 1. Vertical shift =? \n" ); document.write( "
Algebra.Com's Answer #275026 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "For:\r\n" );
document.write( "\r\n" );
document.write( "f(x) = Asin(Bx + C) + D\r\n" );
document.write( "\r\n" );
document.write( "Amplitude = |A|\r\n" );
document.write( "Period = \"2pi%2FB\"\r\n" );
document.write( "Phase shift = \"C%2FB\", left if \"C%2FB\" is positive, right if \"C%2FB\" is negative\r\n" );
document.write( "\r\n" );
document.write( "Vertical shift = D, up if D positive, down if D is negative.\r\n" );
document.write( "\r\n" );
document.write( "---------------------------\r\n" );
document.write( "\r\n" );
document.write( "For:\r\n" );
document.write( "\r\n" );
document.write( "Graph f(x) = sin (x − 2π) − 1\r\n" );
document.write( "\r\n" );
document.write( "f(x) = 1sin(1x + 2p) - 1\r\n" );
document.write( "\r\n" );
document.write( "A = 1, B = 1, C = -2p, D = -1\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Amplitude = |A| = |1| = 1\r\n" );
document.write( "Period = \"2pi%2FB\" = \"2pi%2F1\" = \"2pi\"\r\n" );
document.write( "Phase shift = \"C%2FB\" = \"%28-2%29%2F1\" = -2, right since \"-2\" is negative\r\n" );
document.write( "\r\n" );
document.write( "Vertical shift = D = -1, down since D -1 is negative.\r\n" );
document.write( "\r\n" );
document.write( "---------------------------\r\n" );
document.write( "\r\n" );
document.write( "Graph:  Since the phase shift in absolute value equals the period, the\r\n" );
document.write( "graph of \r\n" );
document.write( "\r\n" );
document.write( "f(x) = sin(x − 2π) − 1\r\n" );
document.write( "\r\n" );
document.write( "is the same as the graph of\r\n" );
document.write( "\r\n" );
document.write( "f(x) = sin(x) − 1\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );