Identifying Functions

Front

What is a function?

Back

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

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 has more than one output.

Front

How can you identify a function from a graph?

Back

A graph represents a function if any vertical line drawn intersects the graph at most once.

Front

What is the vertical line test?

Back

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

Front

If a relation has the pairs (1, 2), (1, 3), (2, 4), is it a function?

Back

No, it is not a function because the input '1' has two different outputs (2 and 3).

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

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 an example of a function?

Back

An example of a function is f(x) = x + 2, where each input x has a unique output.

Front

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

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input '1' has two outputs.