(a) Explanation Given: A function that is decreasing on ( − ∞ , 0 ) ,increasing on ( 0 , ∞ ) and undefined at x = 0 . A function f ( x ) is said to be an increasing function on an interval ( x 1 , x 2 ) , if x 1 < ( o r > ) x 2 implies that f ( x 1 ) < ( o r > ) f ( x 2 ) . A function f ( x ) is said to be decreasing function on an interval ( x 1 , x 2 ) , if x 1 < ( o r > ) (b) To determine To construct: An example for the function that is decreasing on ( − ∞ , 0 ] ,increasing on [ 0 , ∞ ) . (c) To determine To construct: An example for the function that is always positive and always decreasing on all of R.

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3.2, Problem 2C

(a)

To determine

To construct: An example for the function that is decreasing on (−∞,0) ,increasing on (0,∞) and undefined at x=0 .

(b)

To determine

To construct:An example for the function that is decreasing on (−∞,0] ,increasing on [0,∞) .

(c)

To determine

To construct:An example for the function that is always positive and always decreasing on all of R.

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Chapter 3.2, Problem 1C

Chapter 3.2, Problem 3C

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Chapter 3 Solutions

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To construct: An example for the function that is decreasing on ( − ∞ , 0 ) ,increasing on ( 0 , ∞ ) and undefined at x = 0 .

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To construct: An example for the function that is decreasing on (−∞,0) ,increasing on (0,∞) and undefined at x=0 .

To construct:An example for the function that is decreasing on (−∞,0] ,increasing on [0,∞) .

To construct:An example for the function that is always positive and always decreasing on all of R.

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Chapter 3 Solutions