1. 2-6: Absolute Value Functions
Absolute Value: A function in the form
y = a | x - h| + k
a = concavity (if a is (+) the graph opens up, if a is (-) the graph opens down
h = shift in the graph opposite of the sign in the absolute value left or right
k = shift in the graph up or down in the same direction as the sign

2. Absolute Value Function: A function in the form y = |mx + b| + c (m 0)
y=|x - 2|-1
Example #1
The vertex, or minimum point, is (2, -1).

3. Absolute Value Function: A function of the form y = |mx + b| +c (m 0)
y = -|x + 1|
Example #2
The vertex, or maximum point, is (-1, 0).

4. Absolute Value Functions
Graph y = |x| - 3 by completing the t-table:
x y -2 -1 1 2

5. Absolute Value Functions
Graph y = |x| - 3 by completing the t-table:
x y
y =|-2| -3= -1
y =|-1| -3= -2
y =|0| -3= -3
y =|1| -3= -2
y =|2| -3= -1
The vertex, or minimum point, is (0, -3).

6. Try these -4│x + 6 │ - 3 6. -3│x + 6 │ - 3

7. Direct Variation Function: A linear function in the form y = kx, where k 0.2 4 6 –2 –4 –6 x y
y=2x

8. Constant Function: A linear function in the form y = b.

9. Identity Function: A linear function in the form y = x.

10. Greatest Integer Function: A function in the form y = [x]
Note: [x] means the greatest integer less than or equal to x. For example,
the largest integer less than or equal to -3.5 is -4. 2 4 6 –2 –4 –6 x y
y=[x]

11. Greatest Integer Function: A function in the form y = [x]
Graph y= [x] + 2 by completing the t-table:
x y
y= [-3]+2=-1
y= [-2.75]+2=-1
y= [-2.5]+2=-1
y= [-2.25]+2=-1
y= [-2]+2 =0
y= [-1.75]+2=0
y= [-1.5]+2=0
y= [-1.25]+2=0
y= [-1]+2=1
y= [0]+2=2
y= [1]+2=3
x y -3
-2.75
-2.5
-2.25 -2
-1.75
-1.5
-1.25 -1 1 2 4 6 –2 –4 –6 x y