Question

1. a relation is considered a function if each ________ value has exactly one ________ value.

Explanation:

In the definition of a function, for a relation to be a function, each input (which is the domain element, often represented as the independent variable, typically the \( x \)-value or the "input" value) must correspond to exactly one output (the range element, often represented as the dependent variable, typically the \( y \)-value or the "output" value). So the first blank should be filled with "input" (or "domain", "x", etc.) and the second blank with "output" (or "range", "y", etc.). In the context of a relation (usually between two sets, like the set of \( x \)-values and \( y \)-values in a coordinate system), the key idea is that for every element in the domain (the set of all first elements of the ordered pairs) there is exactly one element in the range (the set of all second elements of the ordered pairs) associated with it. So the standard way to phrase this is that each "input" (or "x") value has exactly one "output" (or "y") value.

Answer:

First blank: input (or domain, x)
Second blank: output (or range, y)