Relations and Functions

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

What is a relation?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output.

Front

How can you determine if a mapping is a function?

Back

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

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

Identify the relation that is NOT a function: {(1,-5), (3,1), (-5,4), (4,-2)}, {(2,7), (3,7), (4,7), (5,8)}, {(1,-5), (-1,6), (1,5), (6,-3)}, {(3,-2), (5,-6), (7,7), (8,8)}

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 an ordered pair?

Back

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

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

Is the following relation a function? {(2,3), (2,4), (3,5)}

Back

NO, because the input '2' is associated with two different outputs (3 and 4).

Front

List the ordered pairs from the relation: Input: 1, 2, 3, 4; Output: 3, 6, 9, 12

Back

(1,3), (2,6), (3,9), (4,12) are the ordered pairs.