2.1: Graphing Absolute Value Functions

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

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

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

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

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

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

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−5 +120 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?

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

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

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