Domain & Range

Front

What is the domain of a function?

Back

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

Front

How do you determine the domain of a graph?

Back

Identify the x-values for which the graph exists; look for any restrictions such as holes or asymptotes.

Front

How do you determine the range of a graph?

Back

Identify the y-values that the graph reaches; consider the highest and lowest points of the graph.

Front

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

Back

Each input (x-value) must correspond to exactly one output (y-value).

Front

What is an example of a function?

Back

f(x) = x^2 is a function because for every x, there is one unique y.

Front

What is the domain of the function f(x) = 1/(x-2)?

Back

The domain is all real numbers except x = 2, since the function is undefined at that point.

Front

What is the range of the function f(x) = x^2?

Back

The range is y ≥ 0, since the output of x^2 is always non-negative.

Front

What is the notation for domain and range?

Back

Domain is often expressed as {x | condition}, and range as {y | condition}.

Front

What is a closed interval in terms of domain?

Back

A closed interval includes its endpoints, denoted as [a, b].