Explanation The given function is P = 36 R ( R 2 + 2 R + 1 ) . It is known that, the points for which the graph crosses each axis is called the intercepts of the graph. Set P = 0 and obtain the x- intercept of the graph as follows: 36 R ( R 2 + 2 R + 1 ) = 0 R = 0 Since the above equation is not satisfied for any value of x , the curve P = 36 R ( R 2 + 2 R + 1 ) does not intercept on R -axis. Set R = 0 in the curve P = 36 R ( R 2 + 2 R + 1 ) and obtain the P- intercept of the graph as follows: Since the curve P = 36 R ( R 2 + 2 R + 1 ) is not defined for R = 0 , the curve P = 36 R ( R 2 + 2 R + 1 ) does not intercept on P -axis. Thus, the given curve has R- intercept and P- intercept. Obtain the symmetry of the given function as follows. Substitute, R = − R in the given equation P = 36 R ( R 2 + 2 R + 1 ) and check the symmetry of the given function as follows: Here, the curve P = 36 R ( R 2 + 2 R + 1 ) is same as P = − 36 R ( R 2 − 2 R + 1 ) . Hence, the curve P = 36 R ( R 2 + 2 R + 1 ) is not symmetric about y -axis. It is to be noted that, the curve P = 36 R ( R 2 + 2 R + 1 ) is not same as − P = 36 R ( R 2 + 2 R + 1 ) . Thus, the curve P = 36 R ( R 2 + 2 R + 1 ) is not symmetric about P -axis. Obtain the asymptotes of the given function as follows. As R → ∞ , the curve P = 36 R ( R 2 + 2 R + 1 ) tends to the graph of P = 0 . Thus, the horizontal asymptote of the graph is P = 0 . Since the function P = 36 R ( R 2 + 2 R + 1 ) is undefined for R = − 1 , the vertical asymptote of the graph is R = − 1 . It is to be noted that, the function P = 36 R ( R 2 + 2 R + 1 ) is defined for all real numbers except R = − 1 . Thus, the domain of the function is ( − ∞ , ∞ ) − { − 1 } . The function P = 36 R ( R 2 + 2 R + 1 ) attains positive as well as negative values. Thus, the range of the function P = 36 R ( R 2 + 2 R + 1 ) is ( − ∞ , 9 ]

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ISBN: 9780134508290

Author: Evans

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Chapter 24.6, Problem 28E

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To sketch: The graph of the function P=36R(R2+2R+1).

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Chapter 24.6, Problem 27E

Chapter 24.6, Problem 29E

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Chapter 24 Solutions

EBK BASIC TECHNICAL MATHEMATICS

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The graph of the function P = 36 R ( R 2 + 2 R + 1 ) .

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To sketch: The graph of the function P=36R(R2+2R+1).

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Chapter 24 Solutions