Relations, Functions, Domain, and Range

Front

What is a relation in mathematics?

Back

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

Front

What is a function?

Back

A function is a special type of relation where each input is paired with exactly one output.

Front

Define domain in the context of functions.

Back

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

Front

Define range in the context of functions.

Back

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

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every input has exactly one output.

Front

Identify the domain of the relation {(3,0), (7,0), (3,5), (7,5)}.

Back

The domain is {3, 7}.

Front

Identify the range of the relation {(3,0), (7,0), (3,5), (7,5)}.

Back

The range is {0, 5}.

Front

What is the vertical line test?

Back

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.

Front

If a relation has the pairs (1,2), (1,3), (2,4), is it a function?

Back

No, because the input 1 is paired with two different outputs (2 and 3).

Front

What is an example of a function?

Back

An example of a function is f(x) = x + 2, where each input x has a unique output.