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

Mathematical modeling can be done by using different types of functions besides from linear.

x f(x)-2

-1

0

1

2

Fill in the table of values for f(x) = | x |

Modeling Part 1: f(x) = A| x | Compare the function f(x) = 2|x| to the parent graph

x f(x)

-2

-1

0

1

2

Compare the function f(x) = 0.5|x| to the parent graph

x f(x)

-2

-1

0

1

2

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

-1

0

1

2

Compare the function f(x) = -0.5|x| to the parent Graph f(x) = | x |

x f(x)

-2

-1

0

1

2

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

-1

0

1

Compare the function f(x) = |x - 2| to the parent graph f(x) = | x |

x f(x)

0

1

2

3

4

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

-1

0

1

2

Compare the function f(x) = | x | + 2 to the parent graph f(x) = | x |

x f(x)

-2

-1

0

1

2

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)

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)

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 |

Write a function that represent this graph.

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

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.