SOLUTION: PLEASE HELP SOLVE THIS CIRCULAR FUNCTIONS AND THEIR GRAPHS: What is the phase shift of F(x)=3 sin (2x-4)? HERE ARE THE POSSIBLE ANSWERS: a)2 right b)2 left c)4 right

Algebra ->  Trigonometry-basics -> SOLUTION: PLEASE HELP SOLVE THIS CIRCULAR FUNCTIONS AND THEIR GRAPHS: What is the phase shift of F(x)=3 sin (2x-4)? HERE ARE THE POSSIBLE ANSWERS: a)2 right b)2 left c)4 right      Log On


   

Question 240804: PLEASE HELP SOLVE THIS CIRCULAR FUNCTIONS AND THEIR GRAPHS:
What is the phase shift of F(x)=3 sin (2x-4)?
HERE ARE THE POSSIBLE ANSWERS:
a)2 right
b)2 left
c)4 right
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
For sin and cos, if you write the equation in the form:
f%28x%29+=+C+%2B+A%2Asin%28B%28x-D%29%29
or
f%28x%29+=+C+%2B+A%2Acos%28B%28x-D%29%29
The numbers you find for A, B, C and D will tell you a lot about the function:
A = the amplitude.
B = 2pi/period or 360/period depending on if you are using radians or degrees
C = the vertical shift
D = the horizontal (or phase shift)

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