Concept explainers
To find the asymptotes of the given function −
Answer to Problem 72SR
The vertical asymptote of the function
Explanation of Solution
Given: Function:
Formula used:
Asymptote is a straight line that can be horizontal, vertical or obliquous that goes closer and closer to a curve which is the graphic of a given function.
The vertical asymptotes will occur at those values of x for which the denominator is equal to zero.
The horizontal asymptote is the leading coefficient (the coefficient of the largest exponent) of the numerator divided by the leading coefficient of the denominator if the degrees of the numerator and denominator are the same.
Calculation:
Given: Function:
Solving above function, we have:
As per the definition of the Vertical asymptotes, we have the denominator as Zero:
Thus, the vertical asymptote of the function
As per the definition of the Horizontal asymptotes, we have:
Horizontal asymptote
Horizontal asymptote
Thus, the Horizontal asymptote of the function
Conclusion:
Hence, the vertical asymptote of the function
Chapter 11 Solutions
Algebra 1
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