1.3
Shifting, Section Reflecting, and Stretching Graphs
29 Course Number
Section 1.3 Shifting, Reflecting, and Stretching Graphs
Instructor Objective: In this lesson you learned how to identify and graph shifts, reflections, and nonrigid transformations of functions. Date
Important Vocabulary
Define each term or concept.
Vertical shift A transformation of the graph of y = f(x), represented by h(x) = f(x) c, in which the graph is shifted upward or downward c units respectively (c is a positive real number). Horizontal shift A transformation of the graph of y = f(x), represented by h(x) = f(x c), in which the graph is shifted to the left or to the right c units respectively (c is a positive real number). Rigid transformations Transformations in which the basic shape of the graph is unchanged. Nonrigid transformations Transformations that cause a distortion (a change in the original shape of the graph). I. Summary of Graphs of Common Functions (Page 100) Sketch an example of each of the six most commonly used functions in algebra. Constant Function
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What you should learn How to recognize graphs of common functions
Identity Function
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Absolute Value Function
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Square Root Function
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x
Larson/Hostetler/Edwards Precalculus: Functions and Graphs, A Graphing Approach, 3rd Edition Student Success Organizer IAE
Copyright Houghton Mifflin Company. All rights reserved.
30 Quadratic Function
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Chapter 1
Functions and Their Graphs
Cubic Function
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x
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II. Vertical and Horizontal Shifts (Pages 101-102) Let c be a positive real number. Complete the following representations of shifts in the graph of y = f (x) : 1) Vertical shift c units upward: h(x) = f(x) + c 2) Vertical shift c units downward: 3) Horizontal shift c units to the right: 4) Horizontal shift c units to the left: Example 1: h(x) = f(x) - c h(x) = f(x - c) h(x) = f(x + c)
What you should learn How to use vertical and horizontal shifts to sketch the graphs of functions
Let f x ( ) = x . Write the equation for the function resulting from a vertical shift of 3 units downward and a horizontal shift of 2 units to the right of the graph of f (x ) . f(x) = | x - 2 | - 3
III. Reflecting Graphs (Pages 103-104) A reflection in the x-axis is a type of transformation of the graph of y = f(x) represented by h(x) = - f(x) . A reflection in
What you should learn How to use reflections to sketch the graphs of functions
the y-axis is a type of transformation of the graph of y = f(x) represented by h(x) = f(- x) .
Example 2: Let f ( x ) = x . Describe the graph of g ( x) = - x in terms of f . The graph of g is a reflection of the graph of f in the x-axis.
Larson/Hostetler/Edwards Precalculus: Functions and Graphs, A Graphing Approach, 3rd Edition Student Success Organizer IAE
Copyright Houghton Mifflin Company. All rights reserved.
Section 1.3
Shifting, Reflecting, and Stretching Graphs
31
IV. Nonrigid Transformations (Page 105) Name three types of rigid transformations: 1) Horizontal shifts 2) Vertical shifts 3) Reflections Rigid transformations change only the graph in the xy-plane. Name two types of nonrigid transformations: 1) Vertical stretch 2) V...