The document discusses periodic functions and how to modify the graph of y=sin(x). It explains that: A represents the amplitude and determines the maximum and minimum y-values. B determines the number of periods but is not the actual period. C represents a phase shift, with a positive C shifting the graph left and a negative C shifting it right. D represents a vertical shift or average value of the function, shifting the entire graph up or down.

1. Hello, in the first class today, all we did was go over the question that we did yesterday, and then did a similar question. Then we looked at some graphs ! y = sin (x) May 17, 2007 Scribe- Periodic Functions

2. Here is an equation: f (x) = A sin B (x - C ) + D This equation indicates all the different changes you can make to the graph y = sin(x) A = Amplitude B = Determines how many periods there are C= Phase Shift D = Sinusoidal Axis

3. A , the AMPLITUDE tells you the distance to travel from the sinusoidal axis to find the y- maximum and y - minimum. EXAMPLE: The black graph is y = sin(x) The red graph is y = 2sin(x) See how the red graph has a max. y value of 2 and a min. y value of -2 . The “ 2 ” in front of the equation “y = 2 sin(x)” tells you that from the starting point on the sinusoidal axis, you must go UP 2 units . The black graph is y = sin(x) The blue graph is y = -2sin(x) The “ -2 ” in front of the equation “y = -2 sin(x)” tells you that from the starting point on the sinusoidal axis, you must go DOWN 2 units . Or you can say that the graph is just flipped over the sinusoidal axis.

4. B , it DETERMINES THE PERIOD , but is NOT the period, according to these formulas: EXAMPLE: So the period of the graph y = sin(2x) is π

5. C , is the phase shift (horizontal shift) of the graph. But watch out for the sign of C . Because if the sign of C is positive (+) that means the graph shifts to the LEFT . If the sign of C is negative ( - ) that means the graph shifts to the RIGHT . EXAMPLE: y = sin(x + 1 ) Shift to the LEFT y = sin(x - 1 ) Shift to the RIGHT

6. D , is the SINUSOIDAL AXIS (learn how to say and spell that word!!!). It also has other names ; vertical shift or average value of function . Y = sin x + 1 That “+1” tells you that you must move the whole graph UP 1 unit . Y = sin x - 2 That “-2” tells you that you must move the whole graph DOWN 2 units.