Consider the example of the states of the United States and their U.S. senators.
ID: 3103298 • Letter: C
Question
- Consider the example of the states of the United States and their U.S. senators. You can say that the senators are not a function of the states because each state has more than one senator. However, you can say that the states are a function of the senators because each senator is associated with only one state.
- Make up your own examples of two real-world sets, with each set having more than one element.
- Discuss how elements of those sets can be paired.
- Explain whether one of the sets can be considered a function of the other.
- Address the following regarding linear and nonlinear functions:
- Explain the difference between a linear and nonlinear function. Point out a specific type of nonlinear function to help explain the difference.
- Are linear/nonlinear equations the same as linear/nonlinear functions? What are the differences you see between equations and functions? Try to emphasize when one would use an equation or a function in a real-life application.
Explanation / Answer
One example might be the final grades of a class. On one hand we have the set of possible grades (A, B, ..., F) and on the other we have the set of all students in the class. Clearly the final grade value of, say, C will correspond to more than one student (i.e., more than one student will have a grade of C in the class), and so it is not a function. However, if we reverse the roles of the sets, each student will have only one final grade, and so this is a function mapping from the set of students to the set of possible grades.