Function, Relations, Domain,and Range

A function is a relation in which each input (or domain value) is associated with exactly one output (or range value).

You can determine if a relation is a function by using the vertical line test: if a vertical line intersects the graph of the relation at more than one point, it is not a function.

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

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

The greatest value in the range of a function is the highest output value that the function can produce for the given domain.

To find the domain of a set of ordered pairs, list all the unique x-values from the pairs.

To find the range of a set of ordered pairs, list all the unique y-values from the pairs.

The vertical line test is a method used to determine if a graph represents a function by checking if any vertical line intersects the graph at more than one point.

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

The greatest value in the range for the function y = -2x + 4 occurs at the smallest x-value in the domain, which is -5, resulting in a maximum output of 14.