Periodic Functions scribe

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) = AsinB(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 =
2sin(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 =
-2sin(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.