State the domain and range of each relation. Then determine whether each relation is a function.

step 1 All right, we need to state the domain and range. The domain, or in other words, the X values, i

State the domain and range of each relation. Then determine...

Key Concepts

Domain

The domain of a relation refers to the complete set of input or independent values for which the relation is defined. In other words, it consists of all the values that you can substitute into the relation without breaking its rules. This concept is fundamental in understanding how the relation operates and what values it can accept.

Range

The range of a relation is the set of all output or dependent values that the relation can produce. This means it includes every possible result obtained by applying the relation to its domain. Understanding the range helps to clarify what outputs one might expect from the relation.

Relation

A relation is any set of ordered pairs, where each pair consists of an input value and an output value. It provides a connection or correspondence between elements of two sets. Relations serve as the basis for more specialized concepts such as functions, and they help in understanding the way two quantities are linked.

Function

A function is a special type of relation where every element in the domain is associated with exactly one element in the range. This unique association means that a function will consistently produce a single output for each input, ensuring that the relation is well-defined and predictable.

Vertical Line Test

The vertical line test is a graphical technique used to determine whether a given relation is a function. By analyzing if any vertical line drawn through the graph intersects it at more than one point, one can decide whether the relation violates the criterion for functions. If a vertical line intersects the graph more than once, the relation is not a function.

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