2. Graphing Absolute Value
Graphing Absolute Value Functions
Step 1: Start with the Parent Function
𝑦 = | 𝑥 |
Notice Vertex is (0, 0)
Domain is all Real Numbers −∞, ∞
Range is all values greater than or equal to zero
[0, ∞)
3. Graphing Absolute Value
Graphing Absolute Value Functions
Step 2: Look for Horizontal Shifts within the
equation
𝑦 = | 𝑥 + ℎ |
If ℎ > 0, graph shifts left
If ℎ < 0 graphs shifts right
Example
𝑦 = | 𝑥 + 2 |
𝑦 = |𝑥|𝑦 = | 𝑥 + 2 |
4. Graphing Absolute Value
Graphing Absolute Value Functions
Step 3: Look for Vertical Shifts within the
equation
𝑦 = 𝑥 + ℎ + 𝑘
If k > 0, graph shifts up
If k < 0 graphs shifts down
Example
𝑦 = 𝑥 + 2 − 1
𝑦 = |𝑥|
𝑦 = | 𝑥 + 2 |
𝑦 = 𝑥 + 2 − 1
5. Graphing Absolute Value
Graphing Absolute Value Functions
The Graph can be reflected vertically by including
a negative leading coefficient
𝑦 = − 𝑥 + ℎ + 𝑘
Example
𝑦 = − 𝑥 + 2 − 1
𝑦 = |𝑥|
𝑦 = | 𝑥 + 2 |
𝑦 = 𝑥 + 2 − 1
𝑦 = − 𝑥 + 2 − 1
