2.6: Absolute Value and Families of Functions. Absolute Value Ex1) Graph y = |x|

Slides:

Advertisements

Similar presentations

1.4 – Shifting, Reflecting, and Stretching Graphs

Advertisements

2-6 Families of Functions

Absolute Value Functions and Graphs Lesson 2-5. Important Terms Parent function: the simplest function with these characteristics. The equations of the.

Parent Function Transformation Students will be able to find determine the parent function or the transformed function given a function or graph.

2-6: Families of Functions

2.6 – Vertical and Horizontal Translations

Transformations to Parent Functions. Translation (Shift) A vertical translation is made on a function by adding or subtracting a number to the function.

Transformation of Functions Recognize graphs of common functions Use shifts to graph functions Use reflections to graph functions Use stretching & shrinking.

Section 2.7 Parent Functions and Transformations

Apply rules for transformations by graphing absolute value functions.

Chapter 2 Functions and Graphs Section 2 Elementary Functions: Graphs and Transformations.

Transformations of functions

2-6 Families of Functions M11.D.2.1.2: Identify or graph functions, linear equations, or linear inequalities on a coordinate plane.

3-2 Families of Graphs Pre Calc A. Parent Graphs.

Math-3 Lesson 1-3 Quadratic, Absolute Value and Square Root Functions

Transformations of Linear and Absolute Value Functions

2.7 Absolute Value Functions and Transformations Parent Function of Absolute Value  F(x)= I x I  Graph is a “v-shape”  2 rays meeting at a vertex V(0,0)

Chapter 8-2 Properties of Exponential Functions

Vocabulary The distance to 0 on the number line. Absolute value 1.9Graph Absolute Value Functions Transformations of the parent function f (x) = |x|.

1. g(x) = -x g(x) = x 2 – 2 3. g(x)= 2 – 0.2x 4. g(x) = 2|x| – 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1.

2.6 Families of Functions Sets of functions, called families, in what each function is a transformation of a special function called the parent. Linear.

Entry Task. 2.6 Families of Functions Learning Target: I can analyze and describe transformations of functions Success Criteria: I can describe the effect.

For each function, evaluate f(0), f(1/2), and f(-2)

Section P.3 Transformation of Functions. The Constant Function.

Section 3-2: Analyzing Families of Graphs A family of graphs is a group of graphs that displays one or more similar characteristics. A parent graph is.

Lesson 2-6 Families of Functions.

2.6 Families of Functions Learning goals

Transformations to Parent Functions

Absolute Value Transformations

Warm-Up 1. On approximately what interval is the function is decreasing. Are there any zeros? If so where? Write the equation of the line through.

Use Absolute Value Functions and Transformations

Parent Functions and Transformations

2.6 Translations and Families of Functions

Do Now: Graph the point and its image in a coordinate plane.

3.2 Families of Graphs Objectives: Identify transformations of simple graphs. Sketch graphs of related functions.

Section 2.5 Transformations.

3.4 Graphs and Transformations

2-6 Families of Functions

Rev Graph Review Parent Functions that we Graph Linear:

Warm Up (3,2), (6,2) (5,6), (-2, -1) (-1, 2), (3, 5)

Parent Functions.

Graph Transformations

Parent Functions and Transformations

Section 1.6 Transformation of Functions

y = x2 Translations and Transformations Summary

2.6: Absolute Value and Families of Functions

2.7 Graphing Absolute Value Functions

Parent Functions and Transformations

Parent Functions.

Transformation rules.

1.5b Combining Transformations

4.2 – Translations of the Graphs of the Sine and Cosine Functions

2-6 Families of Functions

2.7 Graphing Absolute Value Functions

2.1 Transformations of Quadratic Functions

Functions and Transformations

6.4a Transformations of Exponential Functions

1.5b Combining Transformations

Transformations to Parent Functions

Parent Functions and Transformations

Transformations to Parent Functions

Graphic Organizer for Transformations

6.4c Transformations of Logarithmic functions

15 – Transformations of Functions Calculator Required

The graph below is a transformation of which parent function?

Parent Functions and Transformations

What is the NAME and GENERAL EQUATION for the parent function below?

Transformations to Parent Functions

2.6 transformations of functions Parent Functions and Transformations.

Presentation transcript:

2.6: Absolute Value and Families of Functions

Absolute Value Ex1) Graph y = |x|

Terms Family of Functions: Functions with certain common characteristics. (ex: the absolute value functions) Parent Function: Simplest function with these characteristics Translation: Shift horizontally, vertically, or both Stretch: occurs when multiplying the function by a value greater than 1 Shrink: occurs when multiplying the function be a value between 0 and 1 Reflection: Change y values to their opposites when reflecting of the x axis

Transformations (the whole enchilada) #2: horizontal translation (opposite) #3: vertical translation #1: vertical stretch (|a| > 1) or shrink (0 < |a| < 1) *negative: vertical reflection Parent function y = |x| Key points (-1, 1), (0, 0), (1, 1)

Describe Describe, in order, the sequence of transformations of each function and then graph the function by hand.

Write the Function Write a function rule for each of the graphs below.