1. 2.1: Graphing Absolute Value Functions

3. For 𝑦= 𝑥 ,
Complete the table
Plot the points you found on the coordinate grid to complete the graph.
Complete the following statements:

4. To graph absolute value equations:
𝑓 𝑥 =𝑎 𝑏 𝑥−ℎ +𝑘
Find the vertex, (ℎ,𝑘)
Put this in the middle of your table
Then find two points to the left and right of the vertex

5. Ex: Describe what transformations occurred. Then draw the graph.
𝒈 𝒙 =𝟒|𝒙−𝟓|−𝟐

6. Ex: Describe what transformations occurred. Then draw the graph.
𝒈 𝒙 =− 𝟏 𝟐 𝒙+𝟑 +𝟏

7. Ex: Describe what transformations occurred. Then draw the graph.
𝒈 𝒙 =− 𝟏 𝟓 𝒙+𝟔 +𝟒

8. Ex: Which graph shows the graph of 𝑓 𝑥 =−|𝑥−3|?
(D) Since the function is reflected over the x-axis and moved right 3

9. Ex:
The number of boats B a boat dealer sells in each month of the year from March to December can be modeled by the function 𝐵=−15 𝑡− where 𝑡 is the time in months and 𝑡 = 1 represents January.
Complete the table of values and then graph
the function.
What is the maximum number of sales in one month?
In what month is the maximum reached?
What is the minimum number of sales
in one month? In what month is the
minimum reached?

10. Ex:
(D) since it moved 2 left and 3 down

11. Ex: (-3,0), (-1,0) (0,1) Min: -1 (−∞,∞) [−1,∞) −2,∞ −∞,−2
(−∞,−3)∪(−1,∞)
(−3,−1)
Min: -1

12. Ex:
(B) because the vertex is (3,2) and the graph goes up since there is no reflection (making the vertex a minimum)