'Horizontal shifts' diaporamas de présentation

College Algebra Fifth Edition James Stewart ? Lothar Redlin ? Saleem Watson

College Algebra Fifth Edition James Stewart ? Lothar Redlin ? Saleem Watson. Functions. 3. Transformations of Functions. 3.5. Transformations of Functions. In this section, we study how certain transformations of a function affect its graph.

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Section 2.5

Section 2.5. Transformations of Functions. Overview. In this section we study how certain transformations of a function affect its graph. We will specifically look at: Shifting Reflecting Stretching. Vertical Shifting.

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Objectives

Objectives. Vertical Shifts Up and Down Horizontal Shifts to the Right and Left Reflections of Graphs Stretching and Shrinking of Graphs. Laws for Graphing Shifts. All graphs must be placed on graphing paper. We do not use ruled paper for graphing.

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Lesson 1-3

Lesson 1-3. New Functions from Old Functions - Part 1. https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcTMSNbfIIP8t1Gulp87xLpqX92qAZ_vZwe4Qu308QRANh_v4UHWiw. At this point in time it is important to know and remember certain parent functions and their graphs.

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Chapter 3 Non-Linear Functions and Applications Section 3.2

Chapter 3 Non-Linear Functions and Applications Section 3.2. Section 3.2 Transformations. Vertical and Horizontal Shifts Reflections Stretching and Compressing Graphs of Functions Combining Multiple Transformations to Sketch a Graph Average Rate of Change The Difference Quotient.

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Types of Functions

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Practice with Quick Sketches

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Chapter 2: Analysis of Graphs of Functions

Chapter 2: Analysis of Graphs of Functions. 2.1 Graphs of Basic Functions and Relations; Symmetry 2.2 Vertical and Horizontal Shifts of Graphs 2.3 Stretching, Shrinking, and Reflecting Graphs 2.4 Absolute Value Functions: Graphs, Equations, Inequalities, and Applications

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2.2 Vertical and Horizontal Shifts of Graphs

2.2 Vertical and Horizontal Shifts of Graphs. Quiz. Identify the basic function with a graph as below: . Vertical Shift of graphs. Discussion 1 . y. f (x) = x 2. f (x) = x 2 +1. ? 1 unit. f (x) = x 2 -2. ? 2 unit. x. f (x) = x 2 -5. ? 5 unit. What about shift f(x) up by 10 unit?

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Calculus is something to

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Transformations of Functions

Transformations of Functions. Graphs of Common Functions. See Table 1.4, pg 184. Characteristics of Functions: Domain Range Intervals where its increasing, decreasing, or constant symmetry. y = f ( x ) + c. y = f ( x ). c. c. y = f ( x ). y = f ( x ) - c. Vertical Shifts.

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Families of Graphs

Families of Graphs. In this section, we will study the following topics: The six graphs of commonly used functions Vertical and horizontal shifts (translations) Reflections of graphs Nonrigid transformations (dilations). 1.2 Functions. Six Graphs of Common Functions.

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1.4 Shifts, Reflections, and Stretches

1.4 Shifts, Reflections, and Stretches. 6 Common parent functions. Constant linear absolute value Quadratic cubic square root. Vertical and horizontal shifts. The following changes in the functions y=f(x) will produce the stated shifts in the graph of y=f(x):

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Vertical shifts (up)

Vertical shifts (up). A familiar example:. y-values each increase by 3. Vertical shift up 3:. graph is shifted up 3 units. More vertical shifts (down). Original curve:. y-values each decrease by 5. Vertical shift down 5:. graph is shifted down 5 units. Horizontal shifts (right).

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Basic Graphs

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1.4 Transformations

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Graphing Rational Functions Through Transformations

Graphing Rational Functions Through Transformations. Rational parent function. Vertical and horizontal shifts. The following changes in the functions y=f(x) will produce the stated shifts in the graph of y=f(x): H(x)=f( x-c ) horizontal shift c units to the right

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2.1 Graphs of Basic Functions and Relations; Symmetry

2.1 Graphs of Basic Functions and Relations; Symmetry. Quiz. Fill in the blank below: Given a function f is defined on I, if f increases on I, then for any x 1 <x 2 , f(x 1 )___f(x 2 ). Increasing, Decreasing and constant functions. y. x. y. x. y. x. Basic Functions. Symmetry.

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