Explanation Given information: A function is given as, f ( x ) = − ( x + 1 ) 2 + 1 . Concept used: Let us suppose a function is defined as y = f ( x ) , h , k and a are positive real numbers, then graph transformation is applied as per below rules. Transformation Effect on the graph of f Changes to point on f Vertical shift y = f ( x ) + k y = f ( x ) − k Shift upward k units Shift downward k units Replace ( x , y ) by ( x , y + k ) Replace ( x , y ) by ( x , y − k ) Horizontal shift y = f ( x − h ) y = f ( x + h ) Shift rightward h units Shift leftward h units Replace ( x , y ) by ( x + h , y ) Replace ( x , y ) by ( x − h , y ) Vertical stretch/shrink y = a [ f ( x ) ] Vertical stretch (if a > 1 ) Vertical shrink (if 0 < a < 1 ) Graph is stretched/shrunk vertically by a factor of a . Replace ( x , y ) by ( x , a y ) Horizontal stretch/shrink y = f ( a ⋅ x ) Horizontal shrink (if a > 1 ) Horizontal stretch (if 0 < a < 1 ) Graph is shrunk/stretched horizontally by a factor of 1 a

15th Edition

ISBN: 9780321978929

Author: Martin-Gay

Publisher: PEARSON

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Chapter 19, Problem 42CR

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The graph of the given function.

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Chapter 19, Problem 41CR

Chapter 20.1, Problem 1VRVC

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Chapter 19 Solutions

EBK ALGEBRA FOUNDATIONS

Ch. 19.1 - Prob. 1VRVC Ch. 19.1 - Prob. 2VRVC Ch. 19.1 - Prob. 3VRVC Ch. 19.1 - Prob. 4VRVC Ch. 19.1 - Prob. 5VRVC Ch. 19.1 - Prob. 6VRVC Ch. 19.1 - Prob. 1ES Ch. 19.1 - Prob. 2ES Ch. 19.1 - Prob. 3ES Ch. 19.1 - Prob. 4ES

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The graph of the given function.

Solution Summary: The author explains that a function is defined as y=f(x), h,k and b are positive real numbers, then graph transformation is applied as per below rules.

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The graph of the given function.

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