Explanation Definition used: Horizontal shifts of graphs: If k is a positive real number, the graph of g ( x ) = f ( x − h ) can be obtained by shifting the graph of f ( x ) to the right h units. The graph of g ( x ) = f ( x + h ) can be obtained by shifting the graph of f ( x ) to the left h units. Vertical shifts of graphs: If k is a positive real number, the graph of g ( x ) = f ( x ) + k can be obtained by shifting the graph of f ( x ) upward k units. The graph of g ( x ) = f ( x ) − k can be obtained by shifting the graph of f ( x ) downward k units. Calculation: The given functions are y = x 2 and y = ( x − 2 ) 2 + 3 . By the definition of horizontal shifts of graphs, it is clear that the graph of f ( x ) = ( x − 2 ) 2 can be obtained by shifting the graph of y = x 2 to the right 2 units. The y coordinate of each point on the graph of y = ( x − 2 ) 2 + 3 is 3 units more than the y coordinate of the point of f ( x ) = ( x − 2 ) 2 with the same x -coordinate. By the definition of vertical shifts of graphs, it is clear that the graph of y = ( x − 2 ) 2 + 3 is obtained if the graph of f ( x ) = ( x − 2 ) 2 shifted upward by 3 units

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- for College Algebra in Context

5th Edition

ISBN: 9780135909621

Author: HARSHBARGER, Ronald, YOCCO, Lisa

Publisher: PEARSON

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Chapter 4.1, Problem 17E

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To explain: The process that the graph of y=(x−2)2+3 is obtained by the transformation on the graph y=x2.

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Chapter 4.1, Problem 16E

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MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- for College Algebra in Context

Ch. 4.1 - In Exercises 116, (a) sketch the graph of each...Ch. 4.1 - In Exercises 116, (a) sketch the graph of each...Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - In Exercises 116, (a) sketch the graph of each...Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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The process that the graph of y = ( x − 2 ) 2 + 3 is obtained by the transformation on the graph y = x 2 .

Solution Summary: The author explains the process of obtaining the graph of y=(x-2)2+3 by the transformation.

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