SHIFTS:
f(x) d
________________________
_______________________
y
x f(x)  f(x)+2
-4
-1
0
3
4
(x,y)
Result for the whole graph
_________________________
x
SHIFTS:
x  (x+1) y
-4
-2
-1
0
2
3
f ( x  c)
_____________________
____________________
(x,y)
y
x
Result for the whole graph
_________________________
STRETCH / COMPRESS:
a[f(x)]
__________________________
______________________________
y
x f(x)  f(x)
-4
-1
0
3
4
(x,y)
x
Result for the whole graph
_______________________________
STRETCH / COMPRESS:
f ( bx ) _________________________
______________________________
x  (2x) y
-2
-1
-0.5
0
1
1.5
2
(x,y)
y
x
Result for the whole graph
___________________________
REFLECTIONS
:
- f ( x ) ________________________
_________________________________
x f(x)  f(x)
-4
-1
0
3
4
y
(x,y)
x
Result for the whole graph
_______________________________
REFLECTIONS
:
f ( -x ) ___________________________
_________________________________
x  ( -x) y
-4
-3
0
1
4
(x,y)
y
x
Result for the whole graph
_______________________________
Combined Transformations:
-2 (f (x-1))+3
____________________________________
y
x

y







x























The affect of Transformations on the Domain
y  a f  bx  c    d
Only the argument ____________________
affects the x values
Domain of f :
____________________
y
x
f
(
Find the domain of :
xf ( 2x )
+
1)
f ( -x )
The Calculator and Transformations
y1 =
y2 =
y3 =
Section 1.4.1 Day 1
Unit Circle
Objectives:
After this lesson, you should be
able to:
• label the unit circle
Definition
y
Unit Circle:
A circle with
radius 1 and
center at the
origin of a
rectangular
coordinate
system.
1
-1
1
-1
x
1.
2.
3.
4.
5.
6.
90°
Fold circle into 90° angles
Label quadrants
Draw radii (Mark right side of xaxis darker)
Label ordered pairs
Label degrees from 0° to each
interval
Label the corresponding radian
measure (use fraction always)
Definition
y
Radian:
The length of the
arc on the unit
circle above the
angle. The length
of this arc is a
measure of the
angle in radians.
1
-1
1
-1
x
Radians
1.
2.
3.
4.
Measure radius with string
Measure one radian on arc of
circle
Continue process around
circumference of circle
Label radians from 0 rads to each
interval
1.
2.
3.
4.
45°
Measure 45° angles
Label ordered pairs
Label degrees from 0° to each
interval
Label the corresponding radian
measure (use fraction always)
30°
1.
2.
3.
4.
Measure 30° angles
Label ordered pairs
Label degrees from 0° to each
interval
Label the corresponding radian
measure (use fraction always)
60°
1.
2.
3.
4.
Measure 60° angles
Label ordered pairs
Label degrees from 0° to each
interval
Label the corresponding radian
measure (use fraction always)
Label each point on the circle graph in
degrees and radians.
3
4
 2 2
,


2
2


2
3
 1 3
  ,

2
2



2
(0,1)
 1
3
 ,

32 2 

4
5
6
 3 1
, 

2
2

, 

6  2 2 
0 (1, 0)
11
6
 3 1
,  

2
 2
5
4
2 2
,
)
2 2
  3 1
 ( 1, 0)
7
6
(
 2  2
,


2
2


4
3
 1  3
  ,

2
2


7
4
3
(0, 1)
2
5
3
1  3
 ,

2 2 
 3 1
,  

2
 2
 2  2
,


2
2


Assignment
132-140
147-154