Explanation Given: The function is f ( x ) = x 3 . 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 . Find the zeros of the function. when f ( x ) = 0 . f ( x ) = 0 x 3 = 0 Solve the above equation. x = 0 So, the x − intercept is ( 0 , 0 ) . Thus, the zeros of the function is 0 . Now, draw the graph. Find the points. Put x = − 2 in the given function. f ( − 2 ) = ( − 2 ) 3 = − 8 Put x = − 1 in the given function. f ( − 1 ) = ( − 1 ) 3 = − 1 Put x = 0 in the given function

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 1.1, Problem 60E

To determine

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 59E

Chapter 1.1, Problem 61E

Chapter 1 Solutions

CALCULUS (CLOTH)

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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 that the function f(x)=x 3 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