Which example is a function and which is not? Explain why.
1. Each student takes a selection of art classes.
2. Each student is placed in a math class.
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To determine whether the given examples represent functions or not, we need to examine the criteria of a function.
A function is a relationship between two sets, where each element of the first set (called the domain) is associated with exactly one element of the second set (called the range).
Let's analyze the examples:
1. Each student takes a selection of art classes.
This example is most likely a function. Assuming that each student can take multiple art classes, each student would be associated with a selection of art classes. In other words, every element (student) in the domain is paired with multiple elements (art classes) in the range. Since each student has a defined set of art classes they take, this satisfies the criteria of a function.
2. Each student is placed in a math class.
This example is also a function. Assuming that each student is placed in only one math class, each student would be associated with exactly one math class. In this case, every element (student) in the domain is paired with exactly one element (math class) in the range, satisfying the criteria of a function.
In conclusion, both examples seem to represent functions, as they meet the criteria of having each element in the domain associated with either multiple or exactly one element in the range.