Explanation The given function is C T = 6 C 6 + C . It is known that, the points for which the graph crosses each axis is called the intercepts of the graph. Set C T = 0 and obtain the C- intercept of the graph as follows: 6 C 6 + C = 0 C = 0 Since the above equation is satisfied for the value of C , the curve C T = 6 C 6 + C intercept on C -axis at C = 0 . Set C = 0 in the curve C T = 6 C 6 + C and obtain the y- intercept of the graph as follows: Since the curve C T = 6 C 6 + C is not defined for C = 0 , the curve C T = 6 C 6 + C intercept on C T -axis at C T = 0 . Thus, the given curve has no x- intercept and y- intercept. Obtain the symmetry of the given function as follows. Substitute, C = − C in the given equation C T = 6 C 6 + C and check the symmetry of the given function as follows: Here, the curve C T = 6 C 6 + C is same as C T = − 6 C 6 − C . Hence, the curve C T = 6 C 6 + C is not symmetric about C T -axis. It is to be noted that, the curve C T = 6 C 6 + C is not same as − C T = 6 C 6 + C . Thus, the curve C T = 6 C 6 + C is not symmetric about C -axis. Obtain the asymptotes of the given function as follows. y = 6 As C → − 6 , the curve C T = 6 C 6 + C tends to the graph of C T = ∞ . Thus, the horizontal asymptote of the graph is C T = ∞ . Since the function C T = 6 C 6 + C is undefined for C = − 6 , the vertical asymptote of the graph is C = − 6 . It is to be noted that, the function C T = 6 C 6 + C is defined for all real numbers except C = − 6 . Thus, the domain of the function is ( − ∞ , ∞ ) − { − 6 } . The function C T = 6 C 6 + C attains positive as well as negative values. Thus, the range of the function C T = 6 C 6 + C is ( − ∞ , ∞ ) − { 6 }

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 24.6, Problem 25E

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To sketch: The graph of the function CT=6C6+C and to explain the significance of the horizontal asymptote.

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Chapter 24.6, Problem 24E

Chapter 24.6, Problem 26E

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Chapter 24 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

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The graph of the function C T = 6 C 6 + C and to explain the significance of the horizontal asymptote.

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Chapter 24 Solutions