Function Vs Relation

Front

What is a function?

Back

A function is a relation where each input (domain) has exactly one output (range).

Front

What is a relation?

Back

A relation is a set of ordered pairs, where an input can have multiple outputs.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

Is the set {(1, 2), (1, 3), (2, 4)} a function?

Back

No, because the input '1' has two different outputs (2 and 3).

Front

Is the set {(0, 1), (1, 2), (2, 3)} a function?

Back

Yes, because each input has exactly one output.

Front

What is an example of a function?

Back

f(x) = 2x + 3 is a function because for every x, there is one unique output.

Front

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

Back

The set {(1, 2), (1, 3)} is a relation but not a function.

Front

What does it mean for a function to be one-to-one?

Back

A one-to-one function means that each output is paired with exactly one input.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function; if a vertical line crosses the graph more than once, it is not a function.