Relation vs. Function

Front

What is a function?

Back

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

Front

Is the mapping (2,3), (2,4) a function?

Back

Not a Function - The input 2 has two different outputs (3 and 4).

Front

Is the mapping (1,2), (3,4), (5,6) a function?

Back

Function - Each input has a unique output.

Front

What is the definition of relation?

Back

A relation is a set of ordered pairs, which can include functions but does not require that each input has a unique output.

Front

Which of the following is a function? (1,2), (1,3), (2,2)

Back

Not a Function - The input 1 has two outputs (2 and 3).

Front

Which of the following is a function? (1,2), (2,3), (3,4)

Back

Function - Each input has a unique output.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 1, where each x-value gives one y-value.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a relation is a function; if a vertical line crosses the graph more than once, 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 a function.