Whether the given statement “the graph of a rational function is continuous only when the denominator is a constant polynomial” is true or false?
Answer to Problem 89E
The given statement is false.
Explanation of Solution
Given information:
Given statement “the graph of a rational function is continuous only when the denominator is a constant polynomial”.
The given statement “the graph of a rational function is continuous only when the denominator is a constant polynomial” is not true,
Because the graph of a rational function is continuous when the polynomial in the denominator has no real zeros.
For example: the function
Thus, the graph is continuous.
Hence, the given statement is false.
Chapter 2 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
- 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