SHIFTS: f ( x ) d_______________________________________________

x

y

Result for the whole graph

_________________________

x f(x) f(x)+2 (x,y)-4-1034

SHIFTS: f ( x c)

_____________________

____________________

x

yx (x+1) y (x,y)-4-2-1023

Result for the whole graph

_________________________

STRETCH / COMPRESS:

a [ f ( x ) ] __________________________

______________________________

Result for the whole graph

_______________________________

x

y

x f(x) f(x) (x,y)-4-1034

STRETCH / COMPRESS:

f ( bx ) _________________________

______________________________

Result for the whole graph

___________________________

x

yx (2x) y (x,y)-2-1-0.5011.52

REFLECTIONS:

- f ( x ) ________________________

_________________________________

x f(x) f(x) (x,y)-4-1034

x

y

Result for the whole graph

_______________________________

REFLECTIONS:

f ( -x ) ___________________________

_________________________________

x

y

Result for the whole graph

_______________________________

x ( -x) y (x,y)-4-3014

Combined Transformations:

-2 (f (x-1))+3

____________________________________

x

y

x

y

The affect of Transformations on the Domain

y a f bx c d Only the argument ____________________ affects the x values

f ( x + 1)

x

y

f ( -x )

f ( 2x )

Domain of f : ____________________

Find the domain of :

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

Unit Circle:

A circle with radius 1 and center at the origin of a rectangular coordinate system.

-1 1

-1

1

y

x

90°1. Fold circle into 90° angles2. Label quadrants3. Draw radii (Mark right side of

x-axis darker)4. Label ordered pairs5. Label degrees from 0° to each

interval6. Label the corresponding

radianmeasure (use fraction always)

Definition

-1 1

-1

1

y

x

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.

Radians1. Measure radius with string2. Measure one radian on arc of

circle3. Continue process around

circumference of circle4. Label radians from 0 rads to

each interval

45°1. Measure 45° angles2. Label ordered pairs3. Label degrees from 0° to each

interval4. Label the corresponding

radian measure (use fraction always)

30°1. Measure 30° angles2. Label ordered pairs3. Label degrees from 0° to each

interval4. Label the corresponding

radian measure (use fraction always)

60°1. Measure 60° angles2. Label ordered pairs3. Label degrees from 0° to each

interval4. Label the corresponding

radian measure (use fraction always)

Label each point on the circle graph in degrees and radians.

0 (1,0)

2 2( , )

4 2 2

1 3,

3 2 2

3 1 ,

6 2 2

5 3 1 ,

6 2 2

( 1,0)

(0,1)2

3 (0, 1)

2

3 2 2,

4 2 2

2 1 3,

3 2 2

4 1 3,

3 2 2

5 2 2,

4 2 2

7 3 1 ,

6 2 2

5 1 3,

3 2 2

7 2 2,

4 2 2

11 3 1 ,

6 2 2

Assignment132-140

147-154