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Graph Transformations 6. Name each type of transformation and draw a picture that shows changes to the original graph y = f (x) Note: Use the graphs for f (x) = x² and/or g(x) = sin x to guide your thinking. а. у%3D f(x) + с b. у%3D f(x) — с c. y = f(x – c) shift up c units shift vight by c units shift down c units d. y = f(x+ c) e. y = -f(x) f. y = f(-x) Shift left X-axis y-axis veflection by c uni reflection g. y = cf(x) Explain the difference between 0 1

Graph Transformations 6. Name each type of transformation and draw a picture that shows changes to the original graph y = f (x) Note: Use the graphs for f (x) = x² and/or g(x) = sin x to guide your thinking. а. у%3D f(x) + с b. у%3D f(x) — с c. y = f(x – c) shift up c units shift vight by c units shift down c units d. y = f(x+ c) e. y = -f(x) f. y = f(-x) Shift left X-axis y-axis veflection by c uni reflection g. y = cf(x) Explain the difference between 0 1

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Graph Transformations 6. Name each type of transformation and draw a picture that shows changes to the original graph \( y = f(x) \). Note: Use the graphs for \( f(x) = x^2 \) and/or \( g(x) = \sin x \) to guide your thinking. a. \( y = f(x) + c \) - Transformation: Shift up by \( c \) units b. \( y = f(x) - c \) - Transformation: Shift down by \( c \) units c. \( y = f(x-c) \) - Transformation: Shift right by \( c \) units d. \( y = f(x+c) \) - Transformation: Shift left by \( c \) units e. \( y = -f(x) \) - Transformation: Reflection over the x-axis f. \( y = f(-x) \) - Transformation: Reflection over the y-axis g. \( y = cf(x) \) - Task: Explain the difference between \( 0 < c < 1 \) and \( c > 1 \) **Graph and Diagram Explanation:** The page includes transformations of functions with corresponding visual cues: - Vertical and horizontal shifts are indicated by arrows showing the direction and magnitude. - Reflections are represented with dashed lines showing the original axis and the flipped image.
Transcribed Image Text:Graph Transformations 6. Name each type of transformation and draw a picture that shows changes to the original graph \( y = f(x) \). Note: Use the graphs for \( f(x) = x^2 \) and/or \( g(x) = \sin x \) to guide your thinking. a. \( y = f(x) + c \) - Transformation: Shift up by \( c \) units b. \( y = f(x) - c \) - Transformation: Shift down by \( c \) units c. \( y = f(x-c) \) - Transformation: Shift right by \( c \) units d. \( y = f(x+c) \) - Transformation: Shift left by \( c \) units e. \( y = -f(x) \) - Transformation: Reflection over the x-axis f. \( y = f(-x) \) - Transformation: Reflection over the y-axis g. \( y = cf(x) \) - Task: Explain the difference between \( 0 < c < 1 \) and \( c > 1 \) **Graph and Diagram Explanation:** The page includes transformations of functions with corresponding visual cues: - Vertical and horizontal shifts are indicated by arrows showing the direction and magnitude. - Reflections are represented with dashed lines showing the original axis and the flipped image.
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