2. 2.7 Graphing Absolute Value Functions Objectives: “I can now graph absolute value function with transformations, I can write equations of absolute value graphs, and I fully understand the meaning of absolute values (the distance from zero). I am killin’ it!” Game Plan: –Horizontal Shifts –Vertical Shifts –Slope

3. 2.7 Graphing Absolute Value Functions The absolute value function always makes a ‘V’ shape graph.

4. 2.7 Graphing Absolute Value Functions Do you notice any patterns or rules to transform a function left or right? Using your rule, sketch the following problems on your whiteboards. Horizontal Translation: f(x - h) shifts to the right f(x + h) shifts to the left

5. 2.7 Graphing Absolute Value Functions Write an equation for each graph.

6. 2.7 Graphing Absolute Value Functions Do you notice any patterns or rules to transform a function up or down? Using your rule, sketch the following problems on your whiteboards. Vertical Translation: f(x) + k shifts up f(x) - k shifts down

7. 2.7 Graphing Absolute Value Functions Write an equation for each graph.

8. Translation The graph of y = | x – h | + k is the graph of y = | x | translated h horizontal units and y vertical units. The new vertex is at ( h, k )

9. 2.7 Graphing Absolute Value Functions Reflect graph across the x-axis: f(x) flips the graphs Shifts 3 to the right Shifts 2 up Shifts 2 to the left Shifts 1 up Reflect over x-axis Shifts 3 to the left Shifts 2 down Reflect over x-axis

10. Graphing Absolute Value Functions Graphing y = a | x – h | + k 1.Plot the vertex ( h, k ). 2.Use the a value as slope to plot the points in each direction. (Rise/Run each way) 3.Connect the dots in a V-shape.

11. Exercise Graph the following function f(x) = ½ | x | f ( x ) = -3| x + 1| – 2

12. Exercise 2 Without a graphing calculator, graph the following functions on your whiteboards. 1. y = | x – 2| + 5 2.y = 2| x + 1| – 3 3. f ( x ) = -3| x + 1| – 2

13. Yay for the internet! https://www.khanacademy.org/math/algebr a2/functions_and_graphs/piecewise- functions-tutorial/v/graphs-of-absolute- value-functionshttps://www.khanacademy.org/math/algebr a2/functions_and_graphs/piecewise- functions-tutorial/v/graphs-of-absolute- value-functions http://www.youtube.com/watch?v=UGbFF nk0xjchttp://www.youtube.com/watch?v=UGbFF nk0xjc

14. Homework Pg. 127 –3-18 3’s, 31, 39