Explanation Given: The function is f ( x ) = 1 ( x − 1 ) 2 + 1 . Formula used: A function f is an even function if f ( − x ) = f ( x ) . The even function is symmetrical about y − axis (vertical). A function f is an odd function if f ( − x ) = − f ( x ) . The odd function is symmetrical about the origin (rotational). The function f ( x ) is increasing if x 1 < x 2 such that f ( x 1 ) < f ( x 2 ) . The function f ( x ) is decreasing if x 1 < x 2 such that f ( x 1 ) > f ( x 2 ) . Calculation: The function is f ( x ) = 1 ( x − 1 ) 2 + 1 . Find the zeros of the function. when f ( x ) = 0 . f ( x ) = 0 1 ( x − 1 ) 2 + 1 = 0 Solve the above equation. 1 = 0 This is a contradiction. Thus, there is no zeros of the function. Now, draw the graph. Find the points. Put x = − 2 in the given function. f ( − 2 ) = 1 ( − 2 − 1 ) 2 + 1 = 1 9 + 1 = 0.1 Put x = − 1 in the given function. f ( − 1 ) = 1 ( − 1 − 1 ) 2 + 1 = 1 4 + 1 = 0.2 Put x = 0 in the given function. f ( 0 ) = 1 ( 0 − 1 ) 2 + 1 = 1 1 + 1 = 0

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 1.1, Problem 58E

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Find the zeros of the function $f$ . Also, draw its graph. Use the symmetry and increase/decrease information.

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Chapter 1.1, Problem 57E

Chapter 1.1, Problem 59E

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Chapter 1 Solutions

Calculus - Standalone book

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