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-value) and an output (y-value).

Front

What is a function?

Back

A function is a special type of relation where each input (x-value) is paired with exactly one output (y-value).

Front

How can you determine if a relation is a function?

Back

A relation is a function if no x-value is repeated with different y-values.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

What does it mean if a graph passes the vertical line test?

Back

If a graph passes the vertical line test, it means that for every x-value, there is only one corresponding y-value, indicating that the graph represents a function.

Front

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

Back

The relation {(1,-5), (1,5), (2,3)} is not a function because the x-value 1 is paired with two different y-values.

Front

What is an example of a function?

Back

The relation {(1,2), (2,3), (3,4)} is a function because each x-value is paired with exactly one y-value.

Front

What is the domain of the function f(x) = x^2 for x in [-3, 3]?

Back

The domain is [-3, 3] because these are the x-values for which the function is defined.

Front

What is the range of the function f(x) = x^2 for x in [-3, 3]?

Back

The range is [0, 9] because the minimum value is 0 (when x=0) and the maximum is 9 (when x=3 or x=-3).