Relations & Functions

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x) and an output (y).

Front

What is a function?

Back

A function is a special type of relation where each input has exactly one output.

Front

List the ordered pairs for the function f(x) = 3x.

Back

(1,3), (2,6), (3,9), (4,12)

Front

How can you determine if a graph represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

Which of the following is not a function? {(0,1), (1,2), (2,3), (3,4)}, {(0,2), (1,3), (4,3), (1,2)}, {(1,3), (4,2), (2,0), (3,4)}, {(1,2), (2,2), (3,2), (4,2)}

Back

{(0,2), (1,3), (4,3), (1,2)}

Front

What is the definition of the domain of a function?

Back

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

Front

What is the definition of the range of a function?

Back

The range is the set of all possible output values (y) that a function can produce.

Front

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

Back

Yes, each input has one output.

Front

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

Back

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

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 produced by exactly one input.