1. Absolute Value
Unit 8

2. Graph 𝑦=|𝑥| Call this the PARENT function
X - input
Y - output -2 2 -1 1
Domain: all real numbers
Range: all positive numbers

3. Graph 𝑦=2|𝑥| What happened to the PARENT function?
X - input
Y - output -2 4 -1 2 1
Domain: all real numbers
Range: all positive numbers
Squeezed closer to the y-axis

4. Graph 𝑦= 1 2 |𝑥| What happened to the PARENT function?
X - input
Y - output -2 4 -1 2 1
Domain: all real numbers
Range: all positive numbers
Widened closer to the x-axis

5. Graph 𝑦=|𝑥−2| What happened to the PARENT function?
X - input
Y - output -4 6 -2 4 2
Domain: all real numbers
Range: all positive numbers
Shifted to the right 2

6. Graph 𝑦= 𝑥 −3 What happened to the PARENT function?
X - input
Y - output -4 1 -2 -1 -3 2 4
Domain: all real numbers
Range: y ≥−3
Shifted down 3

7. Graph 𝑦=−|𝑥| What happened to the parent function?
X - input
Y - output -2 -1 1 2
Domain: all real numbers
Range: all negative numbers
Flipped over the x-axis

8. Summary 𝑦=𝑎 𝑥−𝑏 +𝑐 𝑦=𝑎 𝑥 𝑦= 𝑥−𝑏 shifts parent function to the right
If 𝑎≥1 parent function squeezes closer to the y-axis
If 0≤𝑎≤1 (positive fraction) parent function widens towards the x-axis
If −𝑎 parent function flips over the x-axis
𝑦= 𝑥−𝑏 shifts parent function to the right
𝑦= 𝑥+𝑏 shifts parent function to the left
𝑦= 𝑥 +𝑐 shifts parent function up
𝑦= 𝑥 −c shifts parent function down

9. You Try: Graph & state the Domain & Range
𝑦= 𝑥
𝑦= 𝑥 +3
𝑦=2 𝑥
𝑦= 𝑥+2
𝑦=2 𝑥 −3
𝑦=2 𝑥+2 −3
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