a)
To prove : The graph of the function,
a)
Explanation of Solution
Given information : The function is
Proof : The domain of the rational function is all real numbers except the point at which the denominator is 0. Equate the denominator to 0 and find the value of x .
So, the domain of the function is all real numbers except
Use distributive property in the numerator and factorize the numerator.
The function is not defined at
So, at the point
Thus, it is proved that the graph of the rational function is a straight line
b)
To graph : The rational functions,
b)
Explanation of Solution
Given information : The rational functions are
Graph : For the rational function,
So, the domain is all real numbers except at
Factorize the numerator and cancel the common terms.
Substitute
So, at a point
The graph of the rational function will be,
For the rational function,
So, the domain is all real numbers except at
Factorize the numerator and cancel the common terms.
Substitute
So, at a point
The graph of the rational function will be,
For the rational function,
So, the domain is all real numbers except at
Factorize the denominator and cancel the common terms.
Substitute
So, at a point
The graph of the rational function will be,
Interpretation : The graph of a rational function,
The graph of a rational function,
The graph of a rational function,
Chapter 3 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- 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