Warm-up
Describe the transformations.
1. y = - 2 (x + 3)2 - 9
2. y = 4 | x - 2 | + 1
1
[4.5]
Period:
Domain:
Range:
2
Period:
Domain:
Range:
3
Amplitude - The amplitude of y = a sin x and
y = a cos x represents half the distance between
the maximum and minimum values of the function
and is given by
Amplitude = |a|
Transformations |a| > 1
|a| < 1
vertical _________
vertical _________
4
Ex: 1) y = 5cos x
Amp:
List transformations:
5
2) y = sin x
Amp:
List transformations:
6
3. y = ­3cosx
Amp:
List transformations:
7
Period: how long it takes the
graph to start repeating itself
f(x) = sin(bx)
f(x) = cos(bx)
* Make sure b is factored out!!!
When b=1(parent graph), the period is 2π
and count by π/2 on the x-axis.
If b≠1 to find the period, divide 2π by b. Then divide the
new period by 4 to decide what to count by on the x-axis.
Transformations: when |b| > 1 horizontal compression
when |b| < 1 horizontal stretch
8
Examples:
1) f(x) = sin(3x)
Amp:
Period:
x-scale:
List transformations:
9
2. f(x) = 3cos( x)
Amp:
Period:
x-scale:
List transformations:
10
All Transformations!!!!!
Example:
y = cos(2x +
Amp:
Period:
x-scale:
)+3
List transformations:
11
*Now you try:
Example: y = -2sin(
Amp:
Period:
x-scale:
x+ )-2
List transformations:
12
Homework
p. 330,
#s 3-21 mult. of 3,
39, 41, 46, 52, 54 (show work!)
13
Attachments
GRAPHIC ORGANIZER FOR SINE AND COSINE GRAPHS.DOC