Special Functions and Graphs Algebra II …………… Sections 2.7 and 2.8.

Slides:

Advertisements

Similar presentations

1.4 – Shifting, Reflecting, and Stretching Graphs

Advertisements

Learning Objectives for Section 2.2

1 Learning Objectives for Section 2.2 You will become familiar with some elementary functions. You will be able to transform functions using vertical and.

1 Learning Objectives for Section 2.2 You will become familiar with some elementary functions. You will be able to transform functions using vertical and.

Advanced Algebra Notes

Transformation of Functions Section 1.6. Objectives Describe a transformed function given by an equation in words. Given a transformed common function,

Lesson 5-8 Graphing Absolute Value Functions

Monday, September 15 Algebra II

2.7 - Absolute Value Functions and Transformations

Copyright © 2007 Pearson Education, Inc. Slide 2-1 Chapter 2: Analysis of Graphs of Functions 2.1 Graphs of Basic Functions and Relations; Symmetry 2.2.

Relations and Functions Linear Equations Vocabulary: Relation Domain Range Function Function Notation Evaluating Functions No fractions! No decimals!

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

Determine whether a graph is symmetric with respect to the x-axis, the y-axis, and the origin. Determine whether a function is even, odd, or neither even.

Copyright © 2009 Pearson Education, Inc. CHAPTER 2: More on Functions 2.1 Increasing, Decreasing, and Piecewise Functions; Applications 2.2 The Algebra.

Copyright © 2007 Pearson Education, Inc. Slide 2-1.

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

2.4 Use Absolute Value Functions and Transformations

6-8 Graphing Radical Functions

2.7 Graphing Absolute Value Functions The absolute value function always makes a ‘V’ shape graph.

Graph Absolute Value Functions using Transformations

Algebra II Piecewise Functions Edited by Mrs. Harlow.

Graphing Reciprocal Functions

Consider the function: f(x) = 2|x – 2| Does the graph of the function open up or down? 2. Is the graph of the function wider, narrower, or the same.

Pre-Calculus Lesson 3: Translations of Function Graphs Vertical and horizontal shifts in graphs of various functions.

1. 3x + 2 = ½ x – 5 2. |3x + 2| > x – 5 < -3x |x + 2| < 15 Algebra II 1.

Graphing Absolute Value Functions using Transformations.

Absolute–Value Functions

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

Graph and transform absolute-value functions.

3.4 Graphs and Transformations

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

 You should be able to tell when a graph is shifted, reflected, stretched or shrunk. You should also be able identify transformations from an equation.

2.7 Absolute Value Tranformations

2.7 Use Absolute Value Functions

2.8 Absolute Value Functions

Section 3.5 Graphing Techniques: Transformations.

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

Transformation of Functions Sec. 1.7 Objective You will learn how to identify and graph transformations.

2.7 – Use of Absolute Value Functions and Transformations.

Review of Transformations and Graphing Absolute Value

Vocabulary A nonlinear function that can be written in the standard form Cubic Function 3.1Graph Cubic Functions A function where f (  x) =  f (x).

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

Vocabulary The function f(x) = |x| is an absolute value function. The highest of lowest point on the graph of an absolute value function is called the.

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.

Section 9.3 Day 1 Transformations of Quadratic Functions

1 PRECALCULUS Section 1.6 Graphical Transformations.

Algebra 2 5-R Unit 5 – Quadratics Review Problems.

Section 1-5 Graphical Transformations. Section 1-5 vertical and horizontal translations vertical and horizontal translations reflections across the axes.

1.5 Graphical Transformations Represent translations algebraically and graphically.

2.6 Families of Functions Learning goals

Interesting Fact of the Day

Use Absolute Value Functions and Transformations

ALGEBRA II ALGEBRA II HONORS/GIFTED - SECTIONS 2-6 and 2-7 (Families of Functions and Absolute Value Functions) ALGEBRA II HONORS/GIFTED.

2-7 Absolute Value Functions and Graphs

Graph Absolute Value Functions using Transformations

2.6 Translations and Families of Functions

Functions and Their Graphs

I can Shift, Reflect, and Stretch Graphs

Graph Absolute Value Functions using Transformations

Learning Objectives for Section 2.2

Graph Absolute Value Functions using Transformations

Chapter 2: Analysis of Graphs of Functions

y x Lesson 3.7 Objective: Graphing Absolute Value Functions.

2.7 Graphing Absolute Value Functions

2-6 Families of Functions

2.7 Graphing Absolute Value Functions

2.1 Transformations of Quadratic Functions

Graphing Absolute Value Functions

Presentation transcript:

Special Functions and Graphs Algebra II …………… Sections 2.7 and 2.8

SWBAT  identify, graph and write absolute value functions  graph a function based on translations and transformations  graph and find the value of a piecewise defined function  graph the greatest integer function

Vocabulary  absolute value function  vertex  transformation  translation  parent function  reflection  piecewise function  step function

Absolute Value Function  symmetric about y-axis  for every (x, y) there is a point (-x, y)  vertex - point where sides come together  parent function - basic function, vertex is (0, 0)

General Equation  vertex: (h, k)  horizontal shift: x - h = 0  vertical shift: k  shape of graph remains the same

Examples  For each equation, state the vertex, describe the translation and sketch the graph

Transformations  s hape of the graph changes  stretch = more narrow  shrink = wider  vertical stretch: vertical shrink: reflection (about x-axis):

 vertical ___________ by factor of ______  vertex is ___________  find point on each side of vertex

 reflected about _____________  vertical _________ by factor of _______  vertex is __________  two more points

 vertex is ________  reflected about _________  vertical __________ by factor of _______  two more points

Write the equation of the graph

Sketch additional graphs  Use the graph to sketch  (a)  (b)

Piecewise Function  defined by different expressions, each with a separate domain  ex]  Find f(-3) and f(1)

 Graph the function:

 Write a piecewise function from the graph

 Write the piecewise function from the graph

Greatest Integer Function (step function)  greatest integer not larger than the given value