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 }

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn 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 Solutions

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Ch. 24.1 - For the parabola y = 4 − x2, at the point (3, −5)...Ch. 24.1 - Prob. 2PE Ch. 24.1 - Prob. 1E Ch. 24.1 - Prob. 2E Ch. 24.1 - Prob. 3E Ch. 24.1 - Prob. 4E Ch. 24.1 - Prob. 5E Ch. 24.1 - Prob. 6E Ch. 24.1 - Prob. 7E Ch. 24.1 - Prob. 8E

Ch. 24.1 - Prob. 9E Ch. 24.1 - Prob. 10E Ch. 24.1 - Prob. 11E Ch. 24.1 - Prob. 12E Ch. 24.1 - In Exercises 11–14, find the equations of the...Ch. 24.1 - Prob. 14E Ch. 24.1 - Prob. 15E Ch. 24.1 - Prob. 16E Ch. 24.1 - Prob. 17E Ch. 24.1 - Prob. 18E Ch. 24.1 - Prob. 19E Ch. 24.1 - Prob. 20E Ch. 24.1 - Prob. 21E Ch. 24.1 - Where does the normal line to the parabola y = x —...Ch. 24.1 - Prob. 23E Ch. 24.1 - Prob. 24E Ch. 24.1 - A certain suspension cable with supports on the...Ch. 24.1 - Prob. 26E Ch. 24.1 - Prob. 27E Ch. 24.1 - Prob. 28E Ch. 24.1 - Prob. 29E Ch. 24.1 - Prob. 30E Ch. 24.2 - In Example 1, let x1 = 0.3, and find x2. 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Prob. 48RE Ch. 24 - Prob. 49RE Ch. 24 - Prob. 50RE Ch. 24 - Prob. 51RE Ch. 24 - Prob. 52RE Ch. 24 - In Exercises 49–94, solve the given problems. 53....Ch. 24 - Prob. 54RE Ch. 24 - Prob. 55RE Ch. 24 - Prob. 56RE Ch. 24 - The deflection y (in m) of a beam at a horizontal...Ch. 24 - Prob. 58RE Ch. 24 - Prob. 59RE Ch. 24 - Prob. 60RE Ch. 24 - Prob. 61RE Ch. 24 - Prob. 62RE Ch. 24 - In Fig. 24.75, the tension T supports the 40.0-N...Ch. 24 - Prob. 64RE Ch. 24 - Prob. 65RE Ch. 24 - Prob. 66RE Ch. 24 - An analysis of the power output P (in kW/m3) of a...Ch. 24 - The altitude h (in ft) of a certain rocket as a...Ch. 24 - Prob. 69RE Ch. 24 - Prob. 70RE Ch. 24 - Prob. 71RE Ch. 24 - Prob. 72RE Ch. 24 - Prob. 73RE Ch. 24 - A special insulation strip is to be sealed...Ch. 24 - Prob. 75RE Ch. 24 - Prob. 76RE Ch. 24 - Prob. 77RE Ch. 24 - Prob. 78RE Ch. 24 - Prob. 79RE Ch. 24 - Prob. 80RE Ch. 24 - Prob. 81RE Ch. 24 - Prob. 82RE Ch. 24 - Prob. 83RE Ch. 24 - Prob. 84RE Ch. 24 - Prob. 85RE Ch. 24 - Prob. 86RE Ch. 24 - 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Chapter 24 Solutions