Function vs Non Function

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

What is a non-function?

Back

A non-function is a relation where at least one input (x-value) has more than one output (y-value).

Front

How can you determine if a graph represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the vertical line test?

Back

A method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

Front

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

Back

In a mapping, each input must correspond to exactly one output.

Front

What is an example of a function?

Back

The mapping {(1,2), (2,3), (3,4)} is a function because each input has one output.

Front

What is an example of a non-function?

Back

The mapping {(1,2), (1,3), (2,4)} is not a function because the input '1' has two outputs.

Front

If a set of coordinates is {(2,3), (3,4), (2,5)}, is it a function?

Back

No, it is not a function because the input '2' has two outputs (3 and 5).

Front

What is the definition of a relation in mathematics?

Back

A relation is a set of ordered pairs, which can represent a function or a non-function.

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.