§ 8.3 Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions.

Slides:

Advertisements

Similar presentations

Your Transformation Equation y = - a f(-( x ± h)) ± k - a = x-axis reflection a > 1 = vertical stretch 0 < a < 1 = vertical compression -x = y-axis reflection.

Advertisements

Section 2.5 Transformations of Functions. Overview In this section we study how certain transformations of a function affect its graph. We will specifically.

Chapter 3.4 Graphs and Transformations By Saho Takahashi.

Section 1.6 Transformation of Functions

1 The graphs of many functions are transformations of the graphs of very basic functions. The graph of y = –x 2 is the reflection of the graph of y = x.

Shifting Graphs Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 The graphs of many functions are transformations.

1.6 Shifting, Reflecting and Stretching Graphs How to vertical and horizontal shift To use reflections to graph Sketch a graph.

Bellwork: Graph each line: 1. 3x – y = 6 2. Y = -1/2 x + 3 Y = -2

2.8 : Absolute Value Functions What is absolute value? What does the graph of an absolute value function look like? How do you translate an absolute value.

Exponential Functions and Their Graphs 2 The exponential function f with base a is defined by f(x) = a x where a > 0, a  1, and x is any real number.

Function - 2 Meeting 3. Definition of Composition of Functions.

 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:

WHICH TRANSFORMATIONS DO YOU KNOW? ROTATION WHICH TRANSFORMATIONS DO YOU KNOW? ROTATION.

Transformations of Functions. Graphs of Common Functions See Table 1.4, pg 184. Characteristics of Functions: 1.Domain 2.Range 3.Intervals where its increasing,

September 4, General graph shapes Think about splitting up the domain Draw both separately before you put them together if it helps you to visualize.

Vertical and Horizontal Shifts of Graphs.  Identify the basic function with a graph as below:

Copyright © Cengage Learning. All rights reserved. Pre-Calculus Honors 1.3: Graphs of Functions HW: p.37 (8, 12, 14, all, even, even)

Digital Lesson Shifting Graphs.

FUNCTION TRANSLATIONS ADV151 TRANSLATION: a slide to a new horizontal or vertical position (or both) on a graph. f(x) = x f(x) = (x – h) Parent function.

Shifting Graphs. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. As you saw with the Nspires, the graphs of many functions are transformations.

2.5 Shifting, Reflecting, and Stretching Graphs. Shifting Graphs Digital Lesson.

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

Lesson 3.2. Parent Function General Formula We can write all parent functions in the following form:

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 1.4 Transformations and Operations on Functions.

1 PRECALCULUS Section 1.6 Graphical Transformations.

Transforming Linear Functions

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|

Transforming Linear Functions

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Chapter 2 Functions and Graphs

Transformation of Functions

Absolute Value Functions

Parent Functions and Transformations

2.6 Translations and Families of Functions

Chapter 2 Functions and Graphs

Chapter 2: Analysis of Graphs of Functions

Learning Objectives for Section 2.2

Objectives Transform quadratic functions.

Who Wants to Be a Transformation Millionaire?

Transformations of exponential functions

True or False: Suppose the graph of f is given

Elementary Functions: Graphs and Transformations

Graphing Exponential Functions

Write each using Interval Notation. Write the domain of each function.

2.7 Graphing Absolute Value Functions

Transformation rules.

F(x) = a b (x – h) + k.

2.5 Graphing Techniques; Transformations

3.2 Transformations of the Graphs of Functions

Piecewise-Defined Function

Transformation of Functions

2.7 Graphing Absolute Value Functions

6.4a Transformations of Exponential Functions

Determining the Function Obtained from a Series of Transformations.

1.5b Combining Transformations

Translations & Transformations

REFLECTIONS AND SYMMETRY

Warm-up: Common Errors → no-no’s!

Transformation of Functions

6.4c Transformations of Logarithmic functions

2.5 Graphing Techniques; Transformations

LEARNING GOALS FOR LESSON 2.6 Stretches/Compressions

15 – Transformations of Functions Calculator Required

The graph below is a transformation of which parent function?

Transformations.

Transformation of Functions

Parent Functions and Transformations

Warm up honors algebra 2 3/1/19

Presentation transcript:

§ 8.3 Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions

Graphing Piecewise-Defined Functions Example: Graph Graph each “piece” separately. x f (x) = 3x – 1 – 1(closed circle) –1 – 4 –2 – 7 x f (x) = x + 3 1 4 2 5 3 6 Values  0. Values > 0. Continued.

Graphing Piecewise-Defined Functions Example continued: x y x f (x) = 3x – 1 – 1(closed circle) –1 – 4 –2 – 7 (3, 6) Open circle (0, 3) (0, –1) x f (x) = x + 3 1 4 2 5 3 6 (–1, 4) (–2, 7)

Vertical and Horizontal Shifting Vertical Shifts (Upward or Downward) Let k be a Positive Number Graph of Same As Moved g(x) = f(x) + k f(x) k units upward g(x) = f(x)  k k units downward Horizontal Shifts (To the Left or Right) Let h be a Positive Number Graph of Same As Moved g(x) = f(x  h) f(x) h units to the right g(x) = f(x + h) h units to the left

Vertical and Horizontal Shifting Example: x y 5 5 Begin with the graph of f(x) = x2. Shift the original graph downward 3 units. (0, –3)

Vertical and Horizontal Shifting Example: x y 5 5 Begin with the graph of f(x) = |x|. (0, –2) Shift the original graph to the left 2 units.

Reflections of Graphs Reflection about the x-axis The graph of g(x) = – f(x) is the graph of f(x) reflected about the x-axis.

Reflections of Graphs Example: y 5 5 (4, 2) (4, –2) Reflect the original graph about the x-axis.