2.8 Absolute Value Functions

Goals:

To graph absolute value functions

To identify transformations of absolute value functions.

Graphing on TI-83/84 Press Y= Enter equation into

Y= screen For absolute value,

press MATH-RightArrow-1

Be sure to close off parentheses

The general absolute value equation:

y a x b c if -, then Reflection Across the X-axis (RAX)

if a > 1, vertical shrink by a factor of a.

if a < 1, vertical stretch by a factor of a.

if + b, horizontal shift left b.

If – b, horizontal shift right b.

if + c, vertical shift up c.

If – c, vertical shift down c.

Graphing Absolute Value Functions

Graph the vertex Plot two points on either side of the

vertex Use the slope/plug it in and the fact that

the graph is symmetric Connect three points to make a v-

shaped graph

3 33 3

2 11 1

1 34 2

4 4

Domain Range Domain Range

21

3y x

What are the transformations of the following equations?

1)

2)

4 10 3y x

2 5y x

7 14y x

3)

4)

h. shift right 2

v. shift up 5

RAX

h. shift left 7

v. shift down 14

v. stretch by a factor of 2/3

h. shift left 1

RAX

v. shrink by a factor of 4

h. shift right 10

v. shift down 3

Graph the function – name 3 pointsGraph the function – name 3 points

1) y x

x y

Graph the function – name 3 pointsGraph the function – name 3 points

2) y x

x y

Graph the function – name 3 pointsGraph the function – name 3 points

3) 2y x

x y

Graph the function – name 3 pointsGraph the function – name 3 points

4) 3 1y x

x y

State the transformations and then graph the function

Transformations:12 3

2y x

x y

Homework

p. 126

18-25 all

34-36 all