EXPRESSIONS, EQUATIONS AND INEQUALITIES Ch. 2.7 Absolute Value Functions and Graphs EQ: HOW CAN WE...

EQ: HOW CAN WE GRAPH ABSOLUTE VALUE FUNCTIONS? I WILL GRAPH ABSOLUTE VALUE FUNCTIONS.

EXPRESSIONS, EQUATIONS AND

INEQUALITIES

Ch. 2.7Absolute Value Functions and Graphs

EQ: HOW CAN WE GRAPH ABSOLUTE VALUE FUNCTIONS? I WILL GRAPH ABSOLUTE VALUE FUNCTIONS.

BELL WORK

Write an equation for each transformation of y = x^2.

a. Vertical stretch by a factor of 4.

b. Vertical compression by a factor of ¼.

c. Move to the left 5 units, and to up 3 units.

d. Move to the right 3 units, and down 2 units.

EQ: HOW CAN WE GRAPH ABSOLUTE VALUE FUNCTIONS? I WILL GRAPH ABSOLUTE VALUE FUNCTIONS.

2.6 CONTINUED- COMPRESSION/STRETCH

EQ: HOW CAN WE GRAPH ABSOLUTE VALUE FUNCTIONS? I WILL GRAPH ABSOLUTE VALUE FUNCTIONS.

ABSOLUTE VALUE FUNCTIONS AND GRAPHS

READ

We can apply translations, stretches, compressions, and reflections to any parent function f(x). The absolute value function is a particularly good parent function to use for these transformations since it has an easily recognizable V shape.

This lesson discusses vertical stretches and compressions (those in which all y-coordinates are multiplied by a common factor). Make tables of ordered pairs can help you analyze the effects of the transformations on each coordinate.

EQ: HOW CAN WE GRAPH ABSOLUTE VALUE FUNCTIONS? I WILL GRAPH ABSOLUTE VALUE FUNCTIONS.

THE ABSOLUTE VALUE PARENT FUNCTION, F(X)=|X|

EQ: HOW CAN WE GRAPH ABSOLUTE VALUE FUNCTIONS? I WILL GRAPH ABSOLUTE VALUE FUNCTIONS.

GRAPHING AN ABSOLUTE VALUE FUNCTION

EQ: HOW CAN WE GRAPH ABSOLUTE VALUE FUNCTIONS? I WILL GRAPH ABSOLUTE VALUE FUNCTIONS.

GRAPHING AN ABSOLUTE VALUE FUNCTION

Now you try…

What is the graph of the function y = |x| + 2? How is this different from the parent function?

EQ: HOW CAN WE GRAPH ABSOLUTE VALUE FUNCTIONS? I WILL GRAPH ABSOLUTE VALUE FUNCTIONS.

CONCEPT SUMMARY

EQ: HOW CAN WE GRAPH ABSOLUTE VALUE FUNCTIONS? I WILL GRAPH ABSOLUTE VALUE FUNCTIONS.

STOP AND TALK…

Discussion points…

How is the concept about parent functions related to graph absolute value functions?

How is it different?

What technique(s) can be use to graph absolute value functions?

EQ: HOW CAN WE GRAPH ABSOLUTE VALUE FUNCTIONS? I WILL GRAPH ABSOLUTE VALUE FUNCTIONS.

PRACTICE ABSOLUTE VALUE TRANSFORMATIONS

F(X) = |X| Green

F(x) = |X| + 2 Black

F(X) = |X| -5 Light blue

F(X) = -|x| Red

F(X) = ½ |X| Orange

F(X) = 3|X| Brown

F(X) = |X-4| Yellow

F(X) = |X + 3| Pink

EQ: HOW CAN WE GRAPH ABSOLUTE VALUE FUNCTIONS? I WILL GRAPH ABSOLUTE VALUE FUNCTIONS.

CONCEPT SUMMARY

EQ: HOW CAN WE GRAPH ABSOLUTE VALUE FUNCTIONS? I WILL GRAPH ABSOLUTE VALUE FUNCTIONS.

IDENTIFYING TRANSFORMATIONSWithout graphing, what are the vertex and axis of symmetry of the graph of y=3|x-2|+4? How is the parent function transformed?

EQ: HOW CAN WE GRAPH ABSOLUTE VALUE FUNCTIONS? I WILL GRAPH ABSOLUTE VALUE FUNCTIONS.

IDENTIFYING TRANSFORMATIONSWhat are the vertex and axis of symmetry of

Y= -2|x-1| -3?

EQ: HOW CAN WE GRAPH ABSOLUTE VALUE FUNCTIONS? I WILL GRAPH ABSOLUTE VALUE FUNCTIONS.

POSTER PROJECT

Due Monday, 9/14

EQ: HOW CAN WE GRAPH ABSOLUTE VALUE FUNCTIONS? I WILL GRAPH ABSOLUTE VALUE FUNCTIONS.

CLOSURE

(On your bell sheet)

Explain…

How can we graph absolute value functions?

Why are absolute value functions perfect for applying transformations?

How is graphing absolute value functions similar to graphing parabolas? How is it different?