Explanation The given function is y = x 2 − 1 x 3 . 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: x 2 − 1 x 3 = 0 Since the above equation is satisfied for value of x = − 1 , 1 the curve y = x 2 − 1 x 3 intercept on x -axis. Set x = 0 in the curve y = x 2 − 1 x 3 and obtain the y- intercept of the graph as follows: Since the curve y = x 2 − 1 x 3 is not defined for x = 0 , the curve y = x 2 − 1 x 3 does not intercept on y -axis. Thus, the given curve has x- intercept at x = − 1 , 1 and not y- intercept. Obtain the symmetry of the given function as follows. Substitute, x = − x in the given equation y = x 2 − 1 x 3 and check the symmetry of the given function as follows: Here, the curve y = x 2 − 1 x 3 is same as y = − ( x 2 − 1 x 3 ) . Hence, the curve y = x 2 − 1 x 3 is not symmetric about y -axis. It is to be noted that, the curve y = x 2 − 1 x 3 is not same as − y = x 2 − 1 x 3 . Thus, the curve y = x 2 − 1 x 3 is not symmetric about x-axis. Obtain the asymptotes of the given function as follows. As x → ∞ or x → − ∞ , the curve y = x 2 − 1 x 3 tends to the graph is ∞ . Thus, the horizontal asymptote of the graph is y = ∞ . Since the function y = x 2 − 1 x 3 is undefined for x = 0 , the vertical asymptote of the graph is x = 0 . It is to be noted that, the function y = x 2 − 1 x 3 is defined for all real numbers except x = 0 . Thus, the domain of the function is ( − ∞ , ∞ ) − { 0 } . The function y = x 2 − 1 x 3 attains positive and negative values

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 24.6, Problem 12E

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Chapter 24.6, Problem 11E

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Chapter 24 Solutions

Basic Technical Mathematics

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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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The graph of the function y = x 2 − 1 x 3 .

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Chapter 24 Solutions