AFDA SC– Unit 3: Absolute Value+Piecewise Functions Name: _________________
Day 3 Notes: Graphing Absolute Value Functions
Block: _____ Date:_______
Today we will…
• graph absolute value equations with two variables
• describe the shift from a parent function based on given equation
• determine the equation of an absolute value function given a graph
The graph of an absolute value function is always _____________________________
General form for an Absolute Value function: ______________________________
Axis of Symmetry (AOS)
• imaginary vertical line that divides
the graph in half
• Written as 𝑥𝑥 = ℎ
Vertex
• always found on the AOS
• point at which the graph changes
direction
• Maximum or minimum value of the
function
• Written as (ℎ, 𝑘𝑘)
In the calculator:
Absolute Value Parent Function:
𝑓𝑓 (𝑥𝑥) = |𝑥𝑥|
𝒂𝒂 =
Direction:
𝒌𝒌 =
Vertex:
𝒉𝒉 =
AOS:
𝑥𝑥
𝑓𝑓(𝑥𝑥)
Introducing an “a” Value
1. 𝑓𝑓 (𝑥𝑥) = −|𝑥𝑥|
𝒂𝒂 =
Direction:
𝒌𝒌 =
Vertex:
𝒉𝒉 =
𝑓𝑓(𝑥𝑥)
𝑥𝑥
𝑓𝑓(𝑥𝑥)
𝑥𝑥
𝑓𝑓(𝑥𝑥)
AOS:
2. 𝑓𝑓(𝑥𝑥) = 2|𝑥𝑥|
𝒂𝒂 =
Direction:
𝒌𝒌 =
Vertex:
𝒉𝒉 =
AOS:
1
3. 𝑓𝑓 (𝑥𝑥) = 2 |𝑥𝑥|
𝒂𝒂 =
Direction:
𝒌𝒌 =
Vertex:
𝒉𝒉 =
𝑥𝑥
AOS:
How does the “a” value affect the graphs?
How do we talk about the effects?
Introducing an “h” value
1. 𝑓𝑓 (𝑥𝑥) = |𝑥𝑥 − 2|
𝒂𝒂 =
Direction:
𝒌𝒌 =
Vertex:
𝒉𝒉 =
𝑓𝑓(𝑥𝑥)
𝑥𝑥
𝑓𝑓(𝑥𝑥)
AOS:
2. 𝑓𝑓 (𝑥𝑥) = |𝑥𝑥 + 1|
𝒂𝒂 =
Direction:
𝒌𝒌 =
Vertex:
𝒉𝒉 =
𝑥𝑥
AOS:
How does the “h” value affect the graph?
How do we talk about the effects?
Introducing a “k” value
1. 𝑓𝑓 (𝑥𝑥) = |𝑥𝑥| + 4
𝒂𝒂 =
Direction:
𝒌𝒌 =
Vertex:
𝒉𝒉 =
𝑓𝑓(𝑥𝑥)
𝑥𝑥
𝑓𝑓(𝑥𝑥)
AOS:
2. 𝑓𝑓 (𝑥𝑥) = |𝑥𝑥| − 3
𝒂𝒂 =
Direction:
𝒌𝒌 =
Vertex:
𝒉𝒉 =
𝑥𝑥
AOS:
How does the “k” value affect the graph?
How we talk about the effects?
Combination of a, h, and k shifts
𝑓𝑓 (𝑥𝑥) = −|𝑥𝑥 − 2| + 4
𝒂𝒂 =
Direction:
𝒌𝒌 =
Vertex:
𝒉𝒉 =
𝑥𝑥
𝑓𝑓(𝑥𝑥)
𝑥𝑥
𝑓𝑓(𝑥𝑥)
AOS:
Transformations from parent graph?
𝑓𝑓 (𝑥𝑥) = 2|𝑥𝑥 + 1| − 3
𝒂𝒂 =
Direction:
𝒌𝒌 =
Vertex:
𝒉𝒉 =
AOS:
Transformations from parent graph?
𝑓𝑓 (𝑥𝑥) =
𝒂𝒂 =
𝒉𝒉 =
𝒌𝒌 =
1
|𝑥𝑥 + 3|
2
𝑥𝑥
𝑓𝑓(𝑥𝑥)
𝑥𝑥
𝑓𝑓(𝑥𝑥)
Direction:
AOS:
Vertex:
Transformations from parent graph?
𝑓𝑓 (𝑥𝑥) = −3|𝑥𝑥 − 2| + 2
𝒂𝒂 =
Direction:
𝒌𝒌 =
Vertex:
𝒉𝒉 =
AOS:
Transformations from parent graph?
Writing an Equation Based on a Graph
𝒂𝒂 =
Direction:
𝒌𝒌 =
Vertex:
𝒂𝒂 =
Direction:
𝒌𝒌 =
Vertex:
𝒂𝒂 =
Direction:
𝒌𝒌 =
Vertex:
𝒂𝒂 =
Direction:
𝒌𝒌 =
Vertex:
𝒉𝒉 =
AOS:
Equation:
𝒉𝒉 =
AOS:
Equation:
𝒉𝒉 =
AOS:
Equation:
𝒉𝒉 =
Equation:
AOS: