document.write( "Question 1132220: I recently learned that in order to graph any trig function you need to factor the period out of the phase shift. Can someone explain why? I think this has something to do with the multiple x intercepts but I am not sure.
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Algebra.Com's Answer #749187 by greenestamps(13206) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "You aren't saying exactly what you mean; but it is clear what you mean.

\n" ); document.write( "In general, if you have a parent function y = f(x), then the graph of y = f(x-h) is shifted h units to the right, because h is the value of x that makes x-h = 0.

\n" ); document.write( "With trig functions, to find the phase shift, you need to find how far the graph is shifted right or left.

\n" ); document.write( "Given a trig function like

\n" ); document.write( " $\"sin%283x-pi%29\"$

\n" ); document.write( "the phase shift is the value of x that makes (3x-pi) = 0:

\n" ); document.write( " $\"3x-pi+=+0\"$ --> $\"3x+=+pi\"$ --> $\"x+=+pi%2F3\"$

\n" ); document.write( "The phase shift is pi/3.

\n" ); document.write( "In practice, we usually find that phase shift by factoring out the coefficient of x in the function definition:

\n" ); document.write( " $\"sin%283x-pi%29\"$ --> $\"sin%283%28x-pi%2F3%29%29\"$

\n" ); document.write( "This shows that the phase shift is pi/3. That is, the graph is shifted pi/3 units to the right, in exactly the same way that $\"y+=+%28x-2%29%5E2\"$ is the graph of $\"y+=+x%5E2\"$ shifted 2 units to the right. \n" ); document.write( "

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