Explanation Given: The function is f ( x ) = x 3 − 4 x . 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 ) = x 3 − 4 x . Find the zeros of the function. when f ( x ) = 0 . f ( x ) = 0 x 3 − 4 x = 0 Solve the above equation. Take x common. x ( x 2 − 4 ) = 0 Factor the equation by the formula a 2 − b 2 = ( a + b ) ( a − b ) . x ( x + 2 ) ( x − 2 ) = 0 That is: x = 0 or ( x + 2 ) = 0 or ( x − 2 ) = 0 Solve the above equations. x = 0 , − 2 , 2 So, the x − intercepts are ( 0 , 0 ) , ( − 2 , 0 ) and ( 2 , 0 ) . Thus, the zeros of the function is 0 , − 2 and 2 . Now, draw the graph. Find the points. Put x = − 2 in the given function. f ( − 2 ) = ( − 2 ) 3 − 4 ( − 2 ) = − 8 + 8 = 0 Put x = − 1 in the given function. f ( − 1 ) = ( − 1 ) 3 − 4 ( − 1 ) = − 1 + 4 = 3 Put x = 0 in the given function

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 1.1, Problem 55E

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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 54E

Chapter 1.1, Problem 56E

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Chapter 1 Solutions

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Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

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

Solution Summary: The author explains how the function f is symmetrical about the origin.

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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 Solutions