Domain and Range, Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) corresponds to exactly one output (y-value).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph does not represent a function.

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

What does it mean for a set of ordered pairs to represent a function?

Back

A set of ordered pairs represents a function if no two pairs have the same first element (x-value) with different second elements (y-values).

Front

How do you find the range from a set of ordered pairs?

Back

To find the range from a set of ordered pairs, list all the unique second elements (y-values) from the pairs.

Front

What is an example of a function?

Back

An example of a function is the relation {(1, 2), (2, 3), (3, 4)} because each input has a unique output.

Front

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

Back

An example of a relation that is not a function is {(1, 2), (1, 3), (2, 4)} because the input '1' corresponds to two different outputs.

Front

What is the significance of the range in a function?

Back

The range indicates the possible outputs of a function, which helps in understanding the behavior and limitations of the function.