document.write( "Question 1154768: Describe the transformation required to obtain the graph of the function f(x)=sin(x+pi/2); g(x)=sin(x+pi/3) \n" ); document.write( "

Algebra.Com's Answer #777393 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " In the most important and critical part, the answer by the tutor @MathLover1 is TOTALLY and ABSOLUTELY W R O N G.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " I came to bring the correct answer.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Obviously, the first question is how to obtain the plot of the function f(x) = sin(x + pi/2) \r\n" );
document.write( "\r\n" );
document.write( "                                          from the plot of the parent function y(x) = sin(x).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    The plots of the two function are shown in the Figure below.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The ANSWER is: to get the plot of the function y(x) = sin(x + pi/2), \r\n" );
document.write( "\r\n" );
document.write( "               shift the plot of the parent function  by    units to the LEFT.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Plot y(x) = sin(x) (red) and f(x) = sin(x+pi/2) (green)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( ". . . . . . . . . . . . \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The second question is how to obtain the plot of the function f(x) = sin(x + pi/3) \r\n" );
document.write( "\r\n" );
document.write( "                                from the plot of the parent function y(x) = sin(x).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    The plots of the two function are shown in the Figure below.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The ANSWER is: to get the plot of the function y(x) = sin(x + pi/3), \r\n" );
document.write( "\r\n" );
document.write( "               shift the plot of the parent function  by    units to the LEFT.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Plot y(x) = sin(x) (red) and f(x) = sin(x+pi/3) (green)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This knowledge is the cornerstone in the subject, therefore, MEMORIZE this rule:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    if the argument in the formula is shifted to the RIGH, then the plot is shifted to the LEFT.\r\n" );
document.write( "\r\n" );
document.write( "    and vice versa, if the argument in the formula is shifted to the LEFT, then the plot is shifted to the RIGHT.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "If at the exam you will answer as @MathLover1    teaches you, then an UNSATISFACTORY score is GUARANTEED to you. \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The sign    means the same as  .\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );