Explanation Given: The Cartesian equation is, y = x 1 − x 2 (1) Calculation: a) Calculate the domain: Refer the equation (1), the function is defined for all real values of x except for x = ± 1 Hence, the domain of f ( x ) is ℝ \ { 1 , − 1 } . b) Calculate the intercepts: Calculate the value of x -intercept as follows. Substitute 0 for y in the equation (1), 0 = x 1 − x 2 x = 0 Hence the x -intercept is ( 0 , 0 ) . Calculate the y -intercept. Substitute 0 for x in the equation (1), y = 0 1 − 0 2 = 0 Therefore, the y -intercept is ( 0 , 0 ) . c) Calculate the symmetry: Apply negative and positive values for x in the equation (1). Substitute − x in the equation (1), f ( x ) = x 1 − x 2 f ( − x ) = − x 1 − ( − x ) 2 = − x 1 − x 2 Hence, the condition f ( − x ) = − f ( x ) is true. So, the graph of f is symmetric about origin. d) Calculate the asymptotes: Apply the limit that x tends to ∞ in the equation (1), lim x → ∞ y = lim x → ∞ x 1 − x 2 = lim x → ∞ 1 x 1 x 2 − 1 = 0 0 − 1 = 0 Hence, y = 0 is an horizontal asymptote

Essential Calculus: Early Transcendentals

2nd Edition

ISBN: 9781133112280

Author: James Stewart

Publisher: Cengage Learning

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Chapter 4, Problem 18RE

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Essential Calculus: Early Transcendentals

Ch. 4.1 - Explain the difference between an absolute minimum...Ch. 4.1 - Suppose f is a continuous function defined on a...Ch. 4.1 - For each of the numbers a, b, c, d, r, and s,...Ch. 4.1 - For each of the numbers a, b, c, d, r, and s,...Ch. 4.1 - Use the graph to state the absolute and local...Ch. 4.1 - Use the graph to state the absolute and local...Ch. 4.1 - Sketch the graph of a function f that is...Ch. 4.1 - 710 Sketch the graph of a function f that is...Ch. 4.1 - 710 Sketch the graph of a function f that is...Ch. 4.1 - 710 Sketch the graph of a function f that is...

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The curve by plotting x and y coordinates using guidelines of section 4.5.

Solution Summary: The author illustrates the curve by plotting x and y coordinates using guidelines of section 4.5.

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Chapter 4 Solutions