AFDA – Unit 3: Absolute Value and Piecewise Functions Name: _________________
Day 4 Notes: Graphing A.V. Inequalities with 2 Variables Block: _____ Date:_______
Today we will be…
 graphing two variable absolute value inequalities
 describing shifts of the function when compared to the parent
 determining the inequality of an absolute value based on a graph
Recap:
𝑓(𝑥) = 𝑎|𝑥 − ℎ| + 𝑘
Direction: 𝑎+ : graph opens __________
𝒂 = “slope”; vertical stretch/compression
𝑎− : graph opens __________
*If there is no number in front of the
absolute value, 𝑎 =
(reflection)
𝒉 = horizontal _________________ shift
Axis of Symmetry (AOS):
*_________________ sign
*Imaginary ___________ line that
*If there is no value inside the
cuts the graph into mirror images
absolute value with x, ℎ = 0
𝒌 = vertical _________________ shift
Vertex:
*If there is no number behind the
*point at which the graph changes
absolute value, 𝑘 =
_______________
Absolute Value Parent Function:
𝑓(𝑥) = |𝑥|
𝒂=1
Direction: up
𝒉=0
AOS: 𝑥 = 0
𝒌=0
Vertex: (0, 0)
𝑥
𝑓(𝑥)
−2
2
−1
1
0
0
1
1
2
2
Steps for Graphing an Absolute Value Inequality
Identify 𝑎, ℎ, 𝑘
Identify and plot vertex (ℎ, 𝑘)
Identify and plot axis of symmetry 𝑥 = ℎ
Using 𝑎 as the “slope”, plot additional points on either side of your axis of symmetry
 Remember, the graph should be “V” shaped
5. Connect points using a solid or dotted line
 solid line ≥=≤ and dotted line><
6. Shade
 Use a test point, typically (0, 0) unless the graph goes through that point
 If it creates a true statement, shade the area that contains the test point
 If it creates a false statement, shade the area that does NOT contain the
test point
7. Describe translations from parent graph
1.
2.
3.
4.
Example:
1
𝑓(𝑥) > − |𝑥 + 2| + 5
2
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
Translations from parent graph?
Test for Shading
1. 𝑓(𝑥) ≤ 2|𝑥|
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
Translations from parent graph?
Test for Shading
2. 𝑓(𝑥) > |𝑥 − 2|
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
Translations from parent graph?
Test for Shading
3. 𝑓(𝑥) ≥ |𝑥| − 5
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
Translations from parent graph?
Test for Shading
4. 𝑓(𝑥) < 2|𝑥 − 2| − 5
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
Translations from parent graph?
Test for Shading
5. 𝑓(𝑥) ≥ |𝑥 − 2| + 3
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
Translations from parent graph?
Test for Shading
1
6. 𝑓(𝑥) < |𝑥 − 3| − 2
2
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
Translations from parent graph?
Test for Shading
7. 𝑓(𝑥) > −|𝑥 + 5| + 5
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
Translations from parent graph?
Test for Shading
1
8. 𝑓(𝑥) ≤ |𝑥 + 2| − 1
3
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
Translations from parent graph?
Test for Shading
Test for Shading
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
Inequality:
_________________
Test for Shading
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
Inequality:
__________________
Test for Shading
Inequality:
__________________
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
Test for Shading
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
Inequality:
__________________
Test for Shading
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex:
Inequality:
__________________
Test for Shading
Inequality:
__________________
𝒂=
Direction:
𝒉=
AOS:
𝒌=
Vertex: