Functions & Relations/ Domain & Range

Front

What is a function?

Back

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

Front

How can you determine if a relation is a function?

Back

A relation is a function if no two ordered pairs have the same first element (input) with different second elements (outputs).

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

Given the function {(0,1), (1,-3), (2,-4), (-4,1)}, what is the domain?

Back

The domain is {0, 1, 2, -4}.

Front

Given the function {(0,1), (1,-3), (2,-4), (-4,1)}, what is the range?

Back

The range is {1, -3, -4}.

Front

What is an ordered pair?

Back

An ordered pair is a pair of elements (x, y) where 'x' is the first element (input) and 'y' is the second element (output).

Front

What does it mean for a relation to not be a function?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

What is an example of a relation that is not a function?

Back

The relation {(1,-5), (-1,6), (1,5), (6,-3)} is not a function because the input '1' is associated with two different outputs (-5 and 5).

Front

What is the significance of the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function; if any vertical line intersects the curve more than once, the curve is not a function.