a.
Match the graph of the rational function.
a.
Answer to Problem 10PS
Explanation of Solution
Given information:
Match the graph of the rational function
with the given conditions.
Calculation:
Consider the rationl function
Put
Thus, the y-intercept of the function is
Put
Therefore, the x-intercept of the function is
The vertical asymptotes are given by the zeroes of the denominator
Therefore
The horizontal asymptote is given by the ration of the leading coefficients
Thus, the horizontal asymptote is
Consider the following graph
Note that, it has positive vertical asymptote and negative horizontal asymptote. Also it is having positive
Therefore
Hence, option (iii) is the correct answer.
b.
Match the graph of the rational function.
b.
Answer to Problem 10PS
Explanation of Solution
Given information:
Match the graph of the rational function
with the given conditions.
Calculation:
Consider the rationl function
Put
Thus, the y-intercept of the function is
Put
Therefore, the x-intercept of the function is
The vertical asymptotes are given by the zeroes of the denominator
Therefore
The horizontal asymptote is given by the ration of the leading coefficients
Thus, the horizontal asymptote is
Consider the following graph
Note that it has negative vertical asymptote and negative horizontal asymptote. Also, it is having negative
Hence, option (ii)is the correct answer.
c.
Match the graph of the rational function.
c.
Answer to Problem 10PS
Explanation of Solution
Given information:
Match the graph of the rational function
with the given conditions.
Calculation:
Consider the rationl function
Put
Thus, the y-intercept of the function is
Put
Therefore, the x-intercept of the function is
The vertical asymptotes are given by the zeroes of the denominator
Therefore
The horizontal asymptote is given by the ration of the leading coefficients
Thus, the horizontal asymptote is
Consider the following graph
Note that it has negative vertical asymptote and positive horizontal asymptote. Also, it is has negative
Hence,
Hence, option (iv) is the correct answer.
d.
Match the graph of the rational function.
d.
Answer to Problem 10PS
Explanation of Solution
Given information:
Match the graph of the rational function
with the given conditions.
Calculation:
Consider the rationl function
Put
Thus, the y-intercept of the function is
Put
Therefore, the x-intercept of the function is
The vertical asymptotes are given by the zeroes of the denominator
Therefore
The horizontal asymptote is given by the ration of the leading coefficients
Thus, the horizontal asymptote is
Consider the following graph
Note that it has positive vertical asymptote and positive horizontal asymptote. Also, it is has positive
Hence,
Hence, option (i) is the correct answer.
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
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