Explanation The given function is y = 9 x 2 x 2 + 9 . 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: 9 x 2 x 2 + 9 = 0 Since the above the curve y = 9 x 2 x 2 + 9 intercept on x -axis x = 0 . Set x = 0 in the curve y = 9 x 2 x 2 + 9 and obtain the y- intercept of the graph as follows: Since the curve y = 9 x 2 x 2 + 9 is defined for x = 0 , the curve y = 9 x 2 x 2 + 9 intercept on y -axis y = 0 . Thus, the given curve has no x- intercept and y- intercept. Obtain the symmetry of the given function as follows. Substitute, x = − x in the given equation y = 9 x 2 x 2 + 9 and check the symmetry of the given function as follows: Here, the curve y = 9 x 2 x 2 + 9 is same as y = 9 x 2 x 2 + 9 . Hence, the curve y = 9 x 2 x 2 + 9 is symmetric about y -axis. It is to be noted that, the curve y = 9 x 2 x 2 + 9 is not same as − y = 9 x 2 x 2 + 9 . Thus, the curve y = 9 x 2 x 2 + 9 is not symmetric about y -axis. Obtain the asymptotes of the given function as follows. The degree of numerator is equal to the degree of denominator. Hence y = 9 is the horizontal asymptotes. There are no vertical asymptotes because function is defined only for imaginary value. It is to be noted that, the function y = 9 x 2 x 2 + 9 is defined for all values Thus, the domain of the function is ( − ∞ , ∞ ) . The function y = 9 x 2 x 2 + 9 attains always positive values because the denominator x 2 is always positive. Thus, the range of the function y = 9 x 2 x 2 + 9 is ( 0 , 9 )

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Chapter 24.6, Problem 9E

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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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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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