Function or Relation

Front

What is a function?

Back

A function is a relation where every input has only ONE output.

Front

What is a relation?

Back

A relation is a set of ordered pairs, which may or may not be a function.

Front

Is the graph of a vertical line a function?

Back

No, because it fails the vertical line test.

Front

What does the vertical line test determine?

Back

It determines if a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a 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.

Front

What is the domain of a function?

Back

The domain is the set of all possible input values (x-values) for the function.

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) for the function.

Front

What is an example of a function?

Back

f(x) = 2x + 3 is a function because each input x has a unique output.

Front

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

Back

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

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is associated with exactly one input.