![Precalculus](https://www.bartleby.com/isbn_cover_images/9780321716835/9780321716835_largeCoverImage.gif)
Concept explainers
In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line.
![Chapter 3.1, Problem 23AYU, In Problems 21-28, determine whether the given function is linear or nonlinear. If it is linear,](http://dev-ingestion-image-output.s3-website-us-east-1.amazonaws.com/9780135189405/Chapter-3/images/19281-3.1-23sb-question-digital.jpg)
![Check Mark](/static/check-mark.png)
To calculate: Whether the given function is linear or non-linear. If it linear, then we have to determine the equation of the line.
Answer to Problem 23AYU
Solution:
The given function is non-linear.
Explanation of Solution
Given:
The given function is
Formula used:
A function is said to be linear, if it has a constant average rate of change otherwise the function is non-linear.
The formula for finding the average rate of change is
We know that the average rate of change of a linear function is the slope of that function.
Therefore, we can find the equation of the line using the point-slope formula.
Thus, we get
Calculation:
Now, we have to find the average rate of change.
The rate of change between the first and the second row is
The rate of change between the second and the third row is
Here, we can see that the rate of change of the given function differs.
Therefore, the average rate of change is not a constant.
Thus, the given function is non-linear.
Chapter 3 Solutions
Precalculus
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus and Its Applications (11th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Calculus: Early Transcendentals (3rd 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
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)