a.
To determine whether the relation is a function.
The relation represented in the table is a function.
Given:
Given the table representing the relationship existing between the number of grains of the catalyst and the time required to complete the reaction for a specific amount of chemical:
Number of Grains | Number of seconds |
Concept Used:
Function:
Suppose that
Then, a relation
Calculation:
The domain of the relation is given to be the number of grains of the catalyst.
Observe from the table that the domain of the relation is
Also, observe that the relation relates each and every element of
That is, the relation so represented is a function.
Conclusion:
The relation represented in the table is a function.
b.
To determine whether the relation will be a function if its domain and range are interchanged.
The relation obtained by interchanging the domain and range of the original relation is not a function.
Given:
Given the table representing the relationship existing between the number of grains of the catalyst and the time required to complete the reaction for a specific amount of chemical:
Number of Grains | Number of seconds |
Concept Used:
Function:
Suppose that
Then, a relation
Calculation:
Suppose that the domain and the range of the relation are interchanged.
Then, the domain of the relation will be
Now, observe that the element
Thus, the element
That is, the relation obtained by interchanging the domain and range of the original relation is not a function.
Conclusion:
The relation obtained by interchanging the domain and range of the original relation is not a function.
Chapter 2 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education