Explanation The given function is y = 3 x 2 − 1 . It is known that, the points for which the graph crosses each axis is called the intercepts of the graph. Set y = 0 and obtain the x- intercept of the graph as follows: 3 x 2 − 1 = 0 Since the above equation is not satisfied for any value of x , the curve y = 3 x 2 − 1 does not intercept on x -axis. Set x = 0 in the curve y = 3 x 2 − 1 and obtain the y- intercept of the graph as follows: Since the curve y = 3 x 2 − 1 is not defined for x = 0 , the curve y = 3 x 2 − 1 intercept on y -axis at y = − 3 . Thus, the given curve has no x- intercept but at y = − 3 intercept. Obtain the symmetry of the given function as follows. Substitute, x = − x in the given equation y = 3 x 2 − 1 and check the symmetry of the given function as follows: Here, the curve y = 3 x 2 − 1 is same as y = 3 ( − x ) 2 − 1 . Hence, the curve y = 3 x 2 − 1 is symmetric about y -axis. It is to be noted that, the curve y = 3 x 2 − 1 is not same as − y = 3 x 2 − 1 . Thus, the curve y = 3 x 2 − 1 is not symmetric about y -axis. Obtain the asymptotes of the given function as follows. As x → ∞ or x → − ∞ , the curve y = 3 x 2 − 1 tends to the graph of y = 0 . Thus, the horizontal asymptote of the graph is y = 0 . Since the function y = 3 x 2 − 1 is undefined for x = 0 , the vertical asymptote of the graph is x = − 1 , 1 . It is to be noted that, the function y = 3 x 2 − 1 is defined for all real numbers except x = − 1 , 1 . Thus, the domain of the function is ( − ∞ , ∞ ) − { − 1 , 1 }

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

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Chapter 24.6, Problem 11E

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Chapter 24.6, Problem 10E

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Chapter 24 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

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The curve y = 3 x 2 − 1 .

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Chapter 24 Solutions