Representing Relations and Functions

Front

What is a function?

Back

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

Front

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

Back

Yes, because each input has one output.

Front

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

Back

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

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

Is the relation {(2,3), (4,3), (6,3), (8,5)} a function?

Back

Yes, because none of the x-coordinates repeat.

Front

Is the relation {(3,2), (3,4), (5,6), (7,8)} a function?

Back

No, because the x-coordinate 3 repeats.

Front

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

Back

A one-to-one relation means that each input has a unique output and no two inputs share the same output.

Front

What is an example of a function?

Back

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

Front

What is a vertical line test?

Back

A method to determine if a relation is a function by checking if any vertical line intersects the graph more than once.