1. What is the absolute value of a number?

2. What is the absolute value parent function?

3. What kind of transformations can be done to

a graph?

4. How do you graph a linear inequality?

2.7Make a T-chart and graph each problem.

-2

-1

0

1

2

2

1

0

1

2

1. xy 2. 1 xy 2 xy xy2

1 xy 3

x y

-2

-1

0

1

2

-2

-1

0

1

2

-2

-1

0

1

2

-2

-1

0

1

2

x y x y x y

3. 4. 5.

1

0

1

2

3

0

-1

-2

-1

0

1

.5

0

.5

1

6

3

0

3

6

x y

A transformation changes a graph’s size, shape, position or orientation.

A translation shifts a graph horizontally/vertically, but does not change its size, shape, or orientation

EXAMPLE 1Graphing a function of the form y = | x – h | + k

khxay

h moves the graph horizontally – opposite direction

k moves the graph vertically

(h,k) is the vertex of the graph

a stretches/shrinks graph

•If a > 1 it gets skinnier

•If a < 1, it gets wider

•If a is negative, reflected in the x-axis (the graph flips upside down )

Graph y = | x + 4 | – 2.

Compare the graph with the graph of y = | x |.

First, identify and plot the vertex

Plot another point on the graph by substitution, such as (–2, 0). Use symmetry to plot a third point, (– 6, 0)

(h, k) = (– 4, – 2).

The graph of y = | x + 4 | – 2 is the graph of y = | x | translated down 2 units and left 4 units.

EXAMPLE 3Graph y = –2 x – 1 + 3. Compare the graph with the graph of y = x .

Identify and plot the vertex, (h, k) = (1, 3).

y = –2 x – 1 + 3

Flips t

he graph upsid

e down

Shifts

the

grap

h to

the

right

1

Shifts

the

grap

h up

3

Stretch

es th

e gr

aph

verti

cally

by a

facto

r of 2

GUIDED PRACTICE1. y = |x – 2| + 5

(h, k) = (2, 5).

The graph is translated right 2 units and up 5 units

2. y = |x|14

4

1The graph is shrunk vertically by a factor of

3. f (x) = – 3| x + 1| – 2

The graph is reflected over the x-axis, stretched by a factor of 3, translated left 1 unit and down 2 units

Vertex (-1,-2)

Greater than implies the solution includes everything above the line.

Greater than or equal to implies the solution includes the line and everything above the line.

Less than implies the solution lies below the line.

Less than or equal to implies the solution includes the line and everything below the line.

Graph linear inequalities with one variable

a. y < – 3 b. x < 2

Graph linear inequalities with two variables

a. Graph y > – 2x

Graph linear inequalities with two variables

b. Graph 5x – 2y ≤ – 4

Solve for y

5x – 2y ≤ – 4

– 2y ≤ – 5x – 4

22

5 xy

GUIDED PRACTICE

y > –1

Graph

y > –3x

GUIDED PRACTICE

x > –4

Graph

y < 2x +3

x + 3y < 9

3y < -x + 9

33

1 xy

2x – 6y > 9

– 6y > – 2x + 9

2

3

3

1 xy

Graph an absolute value inequality

y > – 2 x – 3 + 4

Graph an absolute value inequality

y > – x + 3 – 2

Graph an absolute value inequality

y < x – 2 + 1

Graph an absolute value inequality

y < 3 x – 1 – 3

GUIDED PRACTICE

HOMEWORK 2.7 p. 127 #3-14

HOMEWORK 2.8p. 135 #7-16(EOP);

17, 18, 22-27