Relations, Functions, Domain and Range

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, typically representing a relationship between two sets of values.

Front

What is a function?

Back

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

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

How do you determine the domain from a graph?

Back

To determine the domain from a graph, identify the x-values that the graph covers.

Front

How do you determine the range from a graph?

Back

To determine the range from a graph, identify the y-values that the graph covers.

Front

What does it mean if a function is defined for all real numbers?

Back

It means that the domain of the function includes every possible real number.

Front

What is an example of a function with a restricted domain?

Back

An example is the square root function, which is only defined for non-negative numbers (x ≥ 0).

Front

What is the difference between open and closed intervals in the context of domain and range?

Back

An open interval does not include its endpoints, while a closed interval includes its endpoints.

Front

What notation is used to represent the domain of a function?

Back

The domain can be represented using interval notation, set notation, or inequalities.