Explanation Given: The function is f ( x ) = 2 x 2 − 4 . 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 ) = 2 x 2 − 4 . Find the zeros of the function. when f ( x ) = 0 . f ( x ) = 0 2 x 2 − 4 = 0 Solve the above equation. 2 x 2 = 4 Divide both sides by 2. x 2 = 2 Take square on both sides. x 2 = 2 Solve the above equation. x = ± 2 So, the x − intercepts are ( − 2 , 0 ) and ( 2 , 0 ) . Thus, the zeros of the function is − 2 and 2 . Now, draw the graph. Find the points. Put x = − 3 in the given function. f ( − 3 ) = 2 ( − 3 ) 2 − 4 = 18 − 4 = 14 Put x = − 2 in the given function. f ( − 2 ) = 2 ( − 2 ) 2 − 4 = 8 − 4 = 4 Put x = − 1 in the given function. f ( − 1 ) = 2 ( − 1 ) 2 − 4 = 2 − 4 = − 2 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 54E

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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 53E

Chapter 1.1, Problem 55E

Chapter 1 Solutions

Calculus - Standalone book

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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 calculates the function f(x) = 2x 2-4 and draws its graph using symmetry and increase/decrease information.

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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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