1. Absolute Value Day 2
Sept. 12 and 15

2. Bell Ringer
On a number line, graph the numbers that satisfy the following:
𝑥−3 ≤3
𝑥+2 ≥6

3. Homework
Out of 20.
Total score divided by 2

4. Absolute Value Graphs

5. Original: 𝑦=𝑎 𝑥−ℎ +𝑘
𝑦= 𝑥

6. Absolute Value Transformations
𝑦=𝑎 𝑥−ℎ +𝑘
𝑎= the slope 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 . If “a” is negative, the V is upside down. If “a” is positive the V is up.
ℎ= how far the graph moves to the left or right. (-)h it moves to the right. (+)h it moves to the left.
𝑘=how far the graph moves up and down. (+)k it moves up. (-)k it moves down.

7. Ex: 𝑦= 𝑥 +1
Up 1

8. Ex: 𝑦=− 𝑥−2 +2
Upside down, right 2, and up 2

9. Ex: 𝑦= 𝑥+3 +1
Left 3 and up 1

10. Activity!
Match the appropriate equation to it’s graph and transformation. You will have 30 minutes to complete.

11. Domain and Range 𝑦=𝑎 𝑥−ℎ +𝑘
Domain for all absolute values is all reals.
Notation: ℝ, or (−∞, ∞)
Range: (y-axis)
If “a” is positive, then 𝑦≥𝑘.
Notation: 𝑘, ∞
If “a” is negative, then 𝑦≤𝑘.
Notation: −∞ , 𝑘

12. For each, give the transformations, domain, range, and graph

13. For each, give the transformations, domain, range, and graph

14. Write the equation of the absolute value graph.
Remember: 𝑦=𝑎 𝑥−ℎ +𝑘
a= slope (positive=up, negative, down)
h= how far left and right
𝑥−ℎ →
𝑥+ℎ ←
k= how far up and down

15. Write the equation of the absolute value graph.