Big Ideas Math Integrated I, 2016
BI
Big Ideas Math Integrated I, 2016 View details
1. Functions
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Exercise 3 Page 103

What makes a relation a function?

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Practice makes perfect

A relation is a set of coordinates. When each value corresponds with exactly one value, the relation is a function. Below we will provide examples of relations that are and are not functions.

A relation that is a function

Any set of ordered pairs in which each corresponds with exactly one is a function. Consider the following relation.
Notice that each of the values and each correspond with only one value. Thus, the relation is a function. Consider another relation:
Again, each value corresponds with exactly one value. Notice that the points and share the same value. The values do not affect if the relation is a function. In other words, it is okay for two values to share one value, as long as each value only correspond to one value. Thus, this relation is a function.

A relation that is not a function

A relation in which at least one value corresponds to more than one value is not a function. Consider the following relation.

Notice that the points and show that the value corresponds to more than one value. Thus, the relation is not a function.