To determine To discuss: The graph of the function y = 9 x + 27 which can be obtained from the graph of the function y = x . Explanation Given: The function is y = 9 x + 27 . Concept used: Shifting of graphs: “Shifting is a rigid translation because it does not change the size and shape of the curve. Shifting is used to move the curve vertically or horizontally without any change in shape and size of the curve.” y = f ( x + a ) and y = f ( x − a ) is a shift of the curve y = f ( x ) horizontally towards negative and positive direction of x axis respectively. y = f ( x ) + a and y = f ( x ) − a is a shift of the curve y = f ( x ) vertically towards positive and negative direction of y axis respectively. Scaling of graph: Scaling is used to change the shape and size of the curve. A vertical scaling multiplies or divides ever y coordinate by a constant while leaving the x coordinate unchanged. y = a ⋅ f ( x ) A horizontal scaling multiplies or divides ever x coordinate by a constant while leaving the y coordinate unchanged. y = f ( b ⋅ x ) Calculation: The given function is y = 9 x + 27 . Transform the function y = 9 x + 27 into a function of the form y = x + a where a can have any real value. y = 9 x + 27 = 9 ⋅ ( x + 3 ) ( Factorize ) = 9 ⋅ x + 3 ( a ⋅ b = a ⋅ b ) = 3 ⋅ x + 3 This implies that 9 x + 27 = 3 ⋅ x + 3 . The graph of y = 3 ⋅ x + 3 is obtained from the graph of y = x in two steps

6th Edition

ISBN: 9780321900760

Author: Rockswold

Publisher: PEARSON EDUCATION (COLLEGE)

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Chapter 4.4, Problem 91E

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To discuss: The graph of the function y=9x+27 which can be obtained from the graph of the function y=x.

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Chapter 4.4, Problem 90E

Chapter 4.4, Problem 92E

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Chapter 4 Solutions

EBK GRAPHICAL APPROACH TO COLLEGE ALGEB

Ch. 4.1 - Provide a short answer to each question. Do not...Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Provide a short answer to each question. Do not...Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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