Absolute Value Day 2 Sept. 12 and 15

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

Homework Out of 20. Total score divided by 2

Absolute Value Graphs

Original: 𝑦=𝑎 𝑥−ℎ +𝑘 𝑦= 𝑥

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.

Ex: 𝑦= 𝑥 +1 Up 1

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

Ex: 𝑦= 𝑥+3 +1 Left 3 and up 1

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

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

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

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

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

Write the equation of the absolute value graph.