Concept explainers
(a)
To analyse: The value of D(1)=0 is true or false.
(a)
Answer to Problem 58E
The value of D(1)=0 is true
Explanation of Solution
Given information:
The graph of a rational function
Formula used:
The vertical asymptote is x = 1.
Calculation:
The Statement is
When
From the graph, the vertical asymptote is x = 1. That is, for x = 1, the denominator is zero and the function is not defined for x = 1.
Therefore, the Statement (a) is true.
Conclusion:
The value of D(1)=0 is true
(b)
To analyse: The degree of N(x) and D(x) being equal is true or false.
(b)
Answer to Problem 58E
The degrees of N (x) and D(x) are equal is true.
Explanation of Solution
Formula used:
The horizontal asymptote y = 2
Calculation:
Since there is a horizontal asymptote y = 2, so the degrees of N (x) and D(x) are equal.
Therefore, the statement (b) is true.
Conclusion:
The degrees of N (x) and D(x) are equal is true.
(c)
To analyse: The ratio of the leading coefficients determines the value of D(x)=1 is true or false.
(c)
Answer to Problem 58E
The ratio of the leading coefficients of N (x) and D(x) is 1 is false.
Explanation of Solution
Formula used:
The horizontal asymptote is y = 2.
Calculation:
The horizontal asymptote is y = 2. That is, the ratio of the leading coefficients of N (x) and
D(x) is 2.
Therefore the statement is false.
Conclusion:
The ratio of the leading coefficients of N (x) and D(x) is 1 is false.
Chapter 2 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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