1. Objective: be able to graph absolute value functions, and identify changes on their graphs POD: Solve and graph the following inequality -2y + 4 < 6x

2. Mathematical modeling can be done by using different types of functions besides from linear. x f( x ) -2 0 1 2 Fill in the table of values for f( x ) = | x |

3. Modeling Part 1: f( x ) = A | x | Compare the function f( x ) = 2| x | to the parent graph x f( x) -2 0 1 2 Compare the function f( x ) = 0.5| x | to the parent graph x f(x) -2 0 1 2

4. Modeling Part 1: f( x ) = A | x | Compare the function f( x ) = -2| x | to the parent Graph f( x ) = | x | x f(x) -2 0 1 2 Compare the function f( x ) = -0.5| x | to the parent Graph f( x ) = | x | x f( x ) -2 0 1 2

5. Modeling Part 2: f( x ) = | x - H | Compare the function f( x ) = | x +1| to the parent graph f(x) = | x | x f(x) -3 -2 0 1 Compare the function f( x ) = | x - 2| to the parent graph f(x) = | x | x f(x) 0 1 2 3 4

6. Modeling Part 3: f( x ) = | x | + K Compare the function f( x ) = | x | - 3 to the parent graph f(x) = | x | x f(x) -2 0 1 2 Compare the function f( x ) = | x | + 2 to the parent graph f(x) = | x | x f(x) -2 0 1 2

7. Modeling Part 4: f( x ) = | x - H | + K g( x ) = ______________ f( x ) = | x | What function is represented by g(x)? For g( x ) : 3. What is line of symmetry? 2. What is the coordinate of the vertex? 1.Describe the movement of the vertex of g( x ) from the parent function f(x)

8. Modeling Part 4: f( x ) = | x - H | + K g( x ) = ______________ f( x ) = | x | What function is represented by g(x)? For g( x ) : 3. What is line of symmetry? 2. What is the coordinate of the vertex? 1.Describe the movement of the vertex of g( x ) from the parent function f(x)

9. Modeling Part 4: f( x ) = A | x - H | + K 2. Compare the graph g(x) to f(x)? Describe the transformations 3. Write a function to represent g(x) 1. What are the coordinates of the vertex for g(x)? g( x ) = ______________ f( x ) = | x |

10. Write a function that represent this graph.

11. A landscaper sketches the design for a triangular shrub protector on graph paper. Write an equation for the shrub protector

12. On the pool table shown you bank the 5 ball of the side at pt. (-1.25,5), you want the ball to go in the pocket at (-5,0) A. Write an equation for the path of the ball B. Do you make the shot? Explain.