Representing Relations and Functions

Front

What is a function?

Back

A function is a relation in which each input (or domain element) is associated with exactly one output (or range element).

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a relation is a function. If a vertical line intersects the graph of the relation at more than one point, then the relation is not a function.

Front

What does it mean if a function has repeating inputs?

Back

If a function has repeating inputs, it means that the same input is associated with more than one output, which violates the definition of a function.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (or 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 (or y-values) that the function can produce.

Front

How can you determine the range of a function given a set of ordered pairs?

Back

To determine the range of a function 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)}, where each input has a unique output.

Front

What is an example of a non-function?

Back

An example of a non-function is the relation {(1,2), (1,3)}, where the input '1' is associated with two different outputs.

Front

What is a one-to-one function?

Back

A one-to-one function is a function in which each output is associated with exactly one input, meaning no two different inputs produce the same output.

Front

What is a many-to-one function?

Back

A many-to-one function is a function where multiple inputs can produce the same output.