Identifying 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

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 more than once, then it is not a function.

Front

What does it mean for a relation to be not a function?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

Give an example of a function using ordered pairs.

Back

{(1,2), (2,3), (3,4)} is a function because each input (x-value) has a unique output (y-value).

Front

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

Back

{(1,2), (1,3), (2,4)} is not a function because the input '1' is associated with two different outputs (2 and 3).

Front

How can you tell if a set of ordered pairs is a function?

Back

A set of ordered pairs is a function if no x-value is repeated with different y-values.

Front

What does it mean for x-values to repeat in a function?

Back

If x-values repeat in a function, it means that the same input is associated with multiple outputs, which violates the definition of a function.

Front

What is the definition of a mapping in mathematics?

Back

A mapping is a relation that assigns each element from one set (domain) to exactly one element in another set (codomain).

Front

What is the significance of the output in a function?

Back

The output in a function is the result obtained after applying the function to an input, and it must be unique for each input.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.