Function Tables and Relations/Functions Review

A function is a relation where each input (x-value) is associated with exactly one output (y-value).

The domain is the set of all possible input values (x-values) for a function.

The range is the set of all possible output values (y-values) for a function.

A relation is a function if no two ordered pairs have the same first element (x-value).

If a mapping is not a function, it means that at least one input (x-value) is associated with more than one output (y-value).

No, it is not a function because the input '1' is associated with two outputs (2 and 4).

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

An example of a function is f(x) = 2x + 3, where each x-value has a unique y-value.

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input '1' has two different outputs.

Domain refers to the set of input values, while range refers to the set of output values.