2-5 Absolute Value Functions and Graphs

cbmxy

xxf )(

Vertex

• Maximum or minimum of the graph

• For the equation, the vertex is at

c

m

b,

cbmxy

Identify the vertex for each function 1. f(x) = | 2x – 5 |

2. f(x) = | 3x + 6 |

3. f(x) = - |x + 1 | - 2

Graphing absolute value functions by making a table

Find the vertex Make a table of values (at least 5!) Graph the function.

Graph and on the same coordinate plane. Determine the similarities and differences in the two graphs.

Find several ordered pairs for each function.

x | x – 3 |

0 3

1 2

2 1

3 0

4 1

5 2

x | x + 2 |

–4 2

–3 1

–2 0

–1 1

0 2

1 3

Graph the points and connect them.

Answer:• The domain of both graphs

is all real numbers.

• The range of both graphs is

• The graphs have the same shape, but different x-intercepts.

• The graph of g (x) is the graph of f (x) translated left 5 units.

Graph

• y = | x – 3 | + 3

X Y

Graph

• y = | 2x + 1 |

X Y

The recommended dietary allowancefor vitamin C is 2 micrograms per day.Write an absolute value function for the differenceBetween the number of micrograms of Vit C you atetoday x and the recommended amount.

X Y

Graph

342

3 xy

X Y

Graph

• y = | -x – 5 |

X Y

Graph

• y = | -3x |

X Y