1. Lesson 5-1 Graphing Absolute Value Functions

2. Daily Learning Target
I will graph and write an equation of an absolute value function
I will describe the translation of the graph of an absolute value function.

3. 5-8 Graphing Absolute Value Functions
The absolute value function always makes a ‘V’ shape graph.

4. 5.8 Graphing Absolute Value Functions
Do you notice any patterns or rules to transform a function left or right?
Horizontal Translation:
f(x - h) shifts to the right
f(x + h) shifts to the left

5. 5-8 Graphing Absolute Value Functions
Do you notice any patterns or rules to transform a function up or down?
Vertical Translation:
f(x) + k shifts up
f(x) - k shifts down

6. 5-8 Graphing Absolute Value Functions
Reflect graph across the x-axis:
f(x) flips the graphs
Shifts 3 to the right
Shifts 2 to the left
Shifts 3 to the left
Shifts 2 up
Shifts 1 up
Shifts 2 down
Reflect over x-axis
Reflect over x-axis

7. Notes Graphing an Absolute Value Function x y 2 1 3 4 8 6 4 2 4 6 83 4 8 6 4 2 4
Vertex:
( 1, 2 ) 6
Axis of Symmetry:
x = 1 8
Slope:
up 2, right/left 1

8. Notes Graphing an Absolute Value Function Graph the function. Vertex:
( -1, 3 )
Axis of Symmetry:
x = -1
Slope:
down 2, right/left 1

9. Notes Graphing an Absolute Value Function Graph the function. Vertex:
( 3, 4 )
Axis of Symmetry:
x = 3
Slope:
up 1, right/left 1

10. Notes Graphing an Absolute Value Function Graph the function. Vertex:
( 0, 5 )
Axis of Symmetry:
x = 0
Slope:
up 1, right/left 1

11. Notes Graphing an Absolute Value Function Graph the function. Vertex:
( 2, 0 )
Axis of Symmetry:
x = 2
Slope:
up 5, right/left 1

12. Notes Graphing an Absolute Value Function Graph the function. Vertex:
( 1, -3 )
Axis of Symmetry:
x = 1
Slope:
down 1, right/left 1

13. Notes Graphing an Absolute Value Function Graph the function. Vertex:
( 0, -2 )
Axis of Symmetry:
x = 0
Slope:
down 1, right/left 1

14. Notes Writing an Absolute Value Function
Write an equation of the graph shown.
Vertex:
( 3, 0 )
Axis of Symmetry:
x = 3
Slope:
down 3, right/left 2

15. Notes Writing an Absolute Value Function
Write an equation of the graph shown.
Vertex:
( 1, -2 )
Axis of Symmetry:
x = 1
Slope:
up 1, right/left 1

16. Note Writing an Absolute Value Function
Write an equation of the graph shown.
Vertex:
( -2, 2 )
Axis of Symmetry:
x = -2
Slope:
down 4, right/left 1