Graphical Transformations

Slides:



Advertisements
Similar presentations
1.4 – Shifting, Reflecting, and Stretching Graphs
Advertisements

1.6 Graph Transformations
Section 1.6 Transformation of Functions
Graphical Transformations!!! Sec. 1.5a is amazing!!!
Section 1.3 Shifting, Reflecting, and Stretching Graphs.
1.6 Shifting, Reflecting and Stretching Graphs How to vertical and horizontal shift To use reflections to graph Sketch a graph.
2.7 Graphing Absolute Value Functions The absolute value function always makes a ‘V’ shape graph.
Copyright © 2011 Pearson, Inc. 1.6 Graphical Transformations.
Graphical Transformations. Quick Review What you’ll learn about Transformations Vertical and Horizontal Translations Reflections Across Axes Vertical.
 Let c be a positive real number. Vertical and Horizontal Shifts in the graph of y = f(x) are represented as follows. 1. Vertical shift c upward:
PreCalculus Chapter 1 Section 6
Chapter 1.4 Shifting, Reflecting, and Stretching Graphs
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.
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.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 1 Homework, Page 124 Find the formulas for f + g, f – g, and fg.
1 PRECALCULUS Section 1.6 Graphical Transformations.
Pre-Cal Chapter 1 Functions and Graphs Section 1.5 Graphical Transformations.
Section 2.5 Transformations Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.
Essential Question: How do you write and sketch an equation of a function based on the parent graph? Students will write a comparison of the equation of.
1.5 Graphical Transformations Represent translations algebraically and graphically.
Shifting, Reflecting, & Stretching Graphs 1.4. Six Most Commonly Used Functions in Algebra Constant f(x) = c Identity f(x) = x Absolute Value f(x) = |x|
Chapter 1 Functions & Graphs Mr. J. Focht PreCalculus OHHS.
Transformation of Functions Lesson 2.5. Operation: Subtract 2 from DV. Transformation: Vertical translation Example #1.
Transformations of Graphs
Modeling and Equation Solving
CHAPTER 2: More on Functions
Homework, Page 135 Find the (x, y) pair for the value of the parameter. 1.
Transformations of Functions
Chapter 1.4 Shifting, Reflecting, and Stretching Graphs
Graphing Technique; Transformations
College Algebra Chapter 2 Functions and Graphs
Graphical Transformations!!!
Transformations of Graphs
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
Copyright © Cengage Learning. All rights reserved.
Absolute Value Functions
Parent Functions and Transformations
2.6 Translations and Families of Functions
Use Absolute Value Functions and Transformations
3.5 Transformations of Graphs
Chapter 2: Analysis of Graphs of Functions
Section 2.5 Transformations.
2.5 Stretching, Shrinking, and Reflecting Graphs
Learning Objectives for Section 2.2
Pre-AP Pre-Calculus Chapter 1, Section 6
Lesson 5-1 Graphing Absolute Value Functions
Transformations of Graphs
Bellwork.
Chapter 2: Analysis of Graphs of Functions
Graph Transformations
College Algebra Chapter 2 Functions and Graphs
Warm-up: Welcome Ticket
y x Lesson 3.7 Objective: Graphing Absolute Value Functions.
2.7 Graphing Absolute Value Functions
Transformation rules.
1.5b Combining Transformations
2-6 Families of Functions
2.7 Graphing Absolute Value Functions
Transformations of Functions
6.4a Transformations of Exponential Functions
1.5 Graphical Transformations
1.5b Combining Transformations
6.4c Transformations of Logarithmic functions
The Absolute Value Function
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?
Presentation transcript:

Graphical Transformations 1.6 Graphical Transformations

What you’ll learn about Transformations Vertical and Horizontal Translations Reflections Across Axes Vertical and Horizontal Stretches and Shrinks Combining Transformations … and why Studying transformations will help you to understand the relationships between graphs that have similarities but are not the same.

Transformations In this section we relate graphs using transformations, which are functions that map real numbers to real numbers. Rigid transformations, which leave the size and shape of a graph unchanged, include horizontal translations, vertical translations, reflections, or any combination of these. Nonrigid transformations, which generally distort the shape of a graph, include horizontal or vertical stretches and shrinks.

Vertical and Horizontal Translations Let c be a positive real number. Then the following transformations result in translations of the graph of y = f(x). Horizontal Translations y = f(x – c) a translation to the right by c units y = f(x + c) a translation to the left by c units Vertical Translations y = f(x) + c a translation up by c units y = f(x) – c a translation down by c units

Example Vertical Translations

Solution

Example Finding Equations for Translations

Solution

Reflections The following transformations result in reflections of the graph of y = f(x): Across the x-axis y = –f(x) Across the y-axis y = f(–x)

Graphing Absolute Value Compositions Given the graph of y = f(x), the graph y = |f(x)| can be obtained by reflecting the portion of the graph below the x-axis across the x-axis, leaving the portion above the x-axis unchanged; the graph of y = f(|x|) can be obtained by replacing the portion of the graph to the left of the y-axis by a reflection of the portion to the right of the y-axis across the y-axis, leaving the portion to the right of the y-axis unchanged. (The result will show even symmetry.)

Stretches and Shrinks

Example Finding Equations for Stretches and Shrinks

Solution

Example Combining Transformations in Order

Solution

Example Combining Transformations in Order

Solution

Solution (continued)

Quick Review

Quick Review Solutions