Expert: Scott A Wilson - 11/21/2011

Question
1.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.
2.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.

Answer
1. Look at pinecones that are still in the tree.
Given a pinecone, it can be seen which tree it is in.
However, given a tree, there could be various numbers of pinecones,
particularly if the tree is not an evergreen, for then there would be none.

2. A linear function is of the form y = mx + b where m and b are constant, x is the variable, and y is the output.  If objects fit this equaion, they are linera.  If they don't, they are not.  As an example, consider a persons height and weight.  The taller they are, the more weight they will have.  However, just because they are a certain weight gives no indication of how tall they are.  If someone is over 300 pounds, they are probably well over 6' tall, but this isn't required.

A straight linear function would be to convert between American and metric measurment.
For example, is something is 32 degrees, it is always 0 degrees centigrade,
since freezing is freezing, no matter what temperature is used.