Domain & Range of Graphs (Set & Interval Notations)

Front

What is the definition of a function?

Back

A function is a relation in which 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 express the domain in set-builder notation?

Back

Set-builder notation expresses the domain as {x | condition on x}, where 'condition on x' describes the values that x can take.

Front

How do you express the range in set-builder notation?

Back

Range in set-builder notation is expressed as {y | condition on y}, where 'condition on y' describes the values that y can take.

Front

What is interval notation?

Back

Interval notation is a way of representing a range of values using intervals, such as (a, b), [a, b), or [a, b].

Front

What does the notation [a, b) mean?

Back

The notation [a, b) means that 'a' is included in the interval (closed), while 'b' is not included (open).

Front

What does the notation (a, b) mean?

Back

The notation (a, b) means that both 'a' and 'b' are not included in the interval (open interval).

Front

What is the significance of the vertical line test?

Back

The vertical line test is a method to determine if a relation is a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the difference between discrete and continuous domains?

Back

Discrete domains consist of distinct, separate values (e.g., integers), while continuous domains include all values within a certain interval (e.g., real numbers).