Function or Not a 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 the definition of 'not a function'?

Back

A relation is not a function if at least one input (x-value) has more than one output (y-value).

Front

How can you determine if a relation is a function using a graph?

Back

If any vertical line intersects the graph at more than one point, the relation is not a function.

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.

Front

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

Back

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

Front

If a relation has the pairs (2, 3), (3, 4), (4, 5), is it a function?

Back

Yes, because each input has exactly one output.

Front

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

Back

A one-to-one function is a function where each output is paired with exactly one input, meaning no two different inputs have the same output.

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 in real life?

Back

An example of a function is a vending machine: each button (input) gives one specific item (output).

Front

What is the domain of a function?

Back

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