1. Graphing Absolute Value Functions

2. Warm-up

3. Constant function
f(x)= ANY NUMBER

4. Identity function
f(x)=x

5. Absolute Value Function Formula
y = A|x-B|+C
When using this formula, the vertex point of an absolute value function is (B, C).
B is the movement left or right
C is the movement up and down

6. If A is between -1 and 1 (not 0) the function will be WIDER than the parent function this is a vertical Shrink
If A is greater than 1 or less than -1 the function will be NARROWER than the parent function this is a vertical stretch.
If A is positive the graph opens up
If A is negative the graph opens down

7. Find the vertex point of these absolute value functions:
y = 3|x-6|+5
y = -2|x+4|-7
y = |-x|+2
y = |-x-1|
y = |x|
(6, 5)
(-4, -7)
(0, 2)
(1, 0)
(0, 0)

8. Graphing with a Table: (4, 2) Graph the function: y = 2|x-4|+2
Step 1: Find the vertex point.
Step 2: Make a table where the vertex point is the middle value.
Step 3: Fill in the table.
Step 4: Plot the points.
(4, 2) X Y 2
2|2-4|+2 = 6 3
2|3-4|+2 = 4 4 5
2|5-4|+2 = 4 6
2|6-4|+2 = 6

9. Graphing with the equation
Graph the function: y = 3|x+1|-4
Step 1: Find the vertex point.
Step 2: Plot the vertex point.
Step 3: Use “m” of the equation to move to the next point.
Step 4: Go back to the vertex point.
Step 5: Use “-m” of the equation to move to the next point.
Step 6: Connect the dots.
(-1, -4)

10. Label the vertex Label 5 points
Label the vertex
Label 5 points
Determine the transformations from the parent function? (up,down,right or left)