Concept explainers
a.
To fill in the gaps: with reference to the provided graph
a.
Answer to Problem 3E
If f is increasing on an interval, then the y -values of the points on the graph increase as the x -values increase. From the graph of f , we see that f is increasing on the interval [1, 2] and [4, 5] .
Explanation of Solution
Given information: if f is increasing on an interval, then the y -values of the points on the graph____ as the x -values increase. From the graph of f , we see that f is increasing on the interval _____ and _____ .
From the provided information, consider,
As f increases the height if the function f ( x ) also increases, thus, y-values of the points on the graph increase as the x-values increase. In the graph provided, f is increasing on the intervals [1, 2] and [4, 5].
Hence, if f is increasing on an interval, then the y -values of the points on the graph increase as the x -values increase. From the graph of f , we see that f is increasing on the interval [1, 2] and [4, 5] .
b.
To fill in the gaps: with reference to the provided graph
b.
Answer to Problem 3E
If f is decreasing on an interval, then the y -values of the points on the graph decrease as the x -values increase. From the graph of f , we see that f is increasing on the interval [2, 4] and [5, 6] .
Explanation of Solution
Given information: If f is decreasing on an interval, then the y- values of the points on the graph ______ as the x -values increases. From the graph, we see that f is decreasing on the interval ____ and ____.
From the provided information, consider,
As f decreases, the height of the function f ( x ) also decreases, thus, y-values of the points on the graph decrease as the x-values increase. In the graph provided, f is increasing on the intervals [2, 3] and [5, 6].
Hence, if f is decreasing on an interval, then the y -values of the points on the graph decrease as the x -values increase. From the graph of f , we see that f is increasing on the interval [2, 4] and [5, 6] .
Chapter 2 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