Concept explainers
a.
To find the domain of the function
Domain:
Given information:
Function:
Explanation:
To find the domain of a function,
Check for the value of
For
So, the domain of the given function is all the real numbers except for
Conclusion:
Therefore, The domain of
b.
To check whether the function
Not continuous at
Given information:
Function:
Explanation:
In subpart (a), it is observed that the function becomes infinity if
Conclusion:
Therefore, the function is not continuous at
c.
To find the vertical and horizontal asymptotes of the function
Vertical asymptote:
Horizontal asymptote:
Given information:
Function:
Calculation:
Vertical asymptotes:
To find vertical asymptotes, put denominator of the given function equal to zero.
Horizontal asymptotes:
As the degree of numerator is equal to the degree of the denominator, consider the variable with the highest degree in both numerator and denominator.
So, the horizontal asymptote is:
Chapter 2 Solutions
Precalculus with Limits: A Graphing Approach
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning