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 )

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 24.6, Problem 10E

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Chapter 24.6, Problem 9E

Chapter 24.6, Problem 11E

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Chapter 24 Solutions

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The curve y = 9 x 2 x 2 + 9 .

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Chapter 24 Solutions