document.write( "Question 240804: PLEASE HELP SOLVE THIS CIRCULAR FUNCTIONS AND THEIR GRAPHS:
\n" ); document.write( "What is the phase shift of F(x)=3 sin (2x-4)?
\n" ); document.write( "HERE ARE THE POSSIBLE ANSWERS:
\n" ); document.write( "a)2 right
\n" ); document.write( "b)2 left
\n" ); document.write( "c)4 right \n" ); document.write( "

Algebra.Com's Answer #176411 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
For sin and cos, if you write the equation in the form:
\n" ); document.write( " $\"f%28x%29+=+C+%2B+A%2Asin%28B%28x-D%29%29\"$
\n" ); document.write( "or
\n" ); document.write( " $\"f%28x%29+=+C+%2B+A%2Acos%28B%28x-D%29%29\"$
\n" ); document.write( "The numbers you find for A, B, C and D will tell you a lot about the function:
\n" ); document.write( "A = the amplitude.
\n" ); document.write( "B = $\"2pi\"$ /period or 360/period depending on if you are using radians or degrees
\n" ); document.write( "C = the vertical shift
\n" ); document.write( "D = the horizontal (or phase shift)

\n" ); document.write( "Your equation is almost in the right form. We just need to factor the 2 in the argument:
\n" ); document.write( " $\"F%28x%29=3+sin+%282x-4%29+=+3sin%282%28x-2%29%29\"$
\n" ); document.write( "Now we can \"read\" the equation:
\n" ); document.write( "A = 3 so the amplitude is 3.
\n" ); document.write( "B = 2 so we could use $\"2+=+2pi\"$ /period to find the period if we wanted it.
\n" ); document.write( "C is missing so it is zero. There is no vertical shift.
\n" ); document.write( "D = 2 so the horizontal or phase shift is 2 (to the right). (A negative D would be a shift to the left.) \n" ); document.write( "

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