HW: Pg. 95-97 # 14-58 eoe, 59

HW: Pg. 103-104 # 8-20 eoe

2.6 Linear Inequalities in Two Variables

2.6 Animated Activity Online

GRAPHING LINEAR INEQUALITIES IN TWO VARIABLES: http://www.classzone.com/cz/books/algebra_2_2007_na/resources/applications/animations/explore_learning/chapter_2/dswmedia/6_5_IneqTwoVar.html

2.6 Linear Inequalities in Two Variables

(4,5) : 5 4

5 5 True, so IS solution.

(-2,1): 1 2

1 1 Fa

2.) 1

1

lse, so NOT soluti .

1

on

y x

1.) 1

1 True, so IS solut

(5,2):

ion.

1 Tru

(

e

1

,

, 2

s

) : 1

o I5 S solution

x

(2,6) : 6 True, so IS solution.

> 5 (0,2): 2 False, so N

3.) 5

5

OT so on.

luti

y

(

4

-

.)

2,

4 9

(3,

-5): (-2)

-8 < -9 False, so NOT soluti

2) : (3)

12 < -9

F

4 9

4 -9

alse, so NOT solution.

on.

x

2.6 Linear Inequalities in Two Variables

2.6 Linear Inequalities in Two Variables

2

5.) 2

2

4

x -2

x

-1 -1

6.

) - -

2

2

y

y

3 3

7

.) 9

3

3

x

x

2.6 Linear Inequalities in Two Variables

(

4

-

.)

2,

4 9

(3,

-5): (-2)

-8 < -9 False, so NOT soluti

2) : (3)

12 < -9

F

4 9

4 -9

alse, so NOT solution.

on.

x

(0,0) : 0 0

0 2 false, shade other r

8.) 2

2

egion

: 2

te

y

s

graph

t

x

y x

1

9.) 42

1 4test (0,0): 0 0

0 < 4 True, so

shade

2

1:

that re

g n.

4

io

2

y x

graph y x

test (0,0) : 0 0

0 -3 True,

so shade that

10.) - 3

-1

regio

-1

3

n

:

3

3

y x

y x

graph y x

2.7 Piecewise Functions

1.) ( ) = -2( )

(5) = 0

5

1

5

-

g

g

2.) ( ) = -( )-2

(0)

0 0

= -2

f

f

3.) ( ) = ( )+1

(0) 4

3

3

=

f

f

4.) ( ) = 3( )+2

(-2)

-2 -

-

2

= 4

g

g

2.7 Piecewise Functions2 , 1

( )3 1, 1

x xf x

x x

a. Use a highlighter to graph vertical lines where the graph "breaks" into pieces.

We will call these "barriers" (Remember, these are NOT part of the graph, but

useful tools to help us draw the function).

Graph the following piecewise functions: Is this a piecewise function?

How do you know?

To Graph the function:

b. Determine what of graph one of the pieces is.

(In this example, ( ) 2 is a line).

type

f x xc. What section of the graph will that be plotted in?

(In this example, ( ) 2 will be plotted on the left piece

because that is where 1.)

f x x

x

d. Will the be an open point ( <, >)or a closed point ( , )?

(In this example, the will be an OPEN circle).

ENDPOINT

ENDPOINT

e. Substitute the into the piece of the function.

(In this example, ( ) 2 ( 1) 2( 1) 2 so the endpoint is (-1, 2)).

ENDPOIN

f x x f

T

f. Substitute another " " value that fits the criteria so that you have another point.

(In this example, 1 so we will choose 2. When we substitute that value

into the equation, we get -4, so the

x

x x next point is (-2,-4) ).

g. Graph the one piece. REMEMBER.... Do not cross through the barrier lines!!!

h. Repeat steps b-g for each of the other pieces of the function.

2.7 Piecewise Functionsa. Draw barriers. b. Select one piece – what type of graph is it?c. Where will it be plotted?d. Is the endpoint open or closed?e. Find and graph the endpointf. Find another point in that sectiong. Graph the one piece. REMEMBER…. Do not cross through the barrier lines!!! h. Repeat steps b-g for each of the other pieces of the function.

2.7 Piecewise Functions

Homework:

Pg. 111-112 # 27-43o, 46, 47

Pg. 117-118 # 13-23o, 27, 35, 37