Functions, Domain and Range

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output (y) for each input (x).

Front

How do you determine the range of a relation?

Back

The range of a relation is the set of all output values (y-values) from the ordered pairs.

Front

Given the relation {(2, 3), (4, 5), (2, 6)}, is this a function?

Back

No, this is not a function because the input '2' is associated with two different outputs (3 and 6).

Front

What is the domain of a function?

Back

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

Front

How can you identify if a relation is a function using the vertical line test?

Back

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

Front

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

Back

A one-to-one relation is a function where each output value is associated with exactly one input value.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represents a point in a coordinate system.

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 difference between a function and a relation?

Back

A relation is any set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.

Front

How do you find the domain of a function from a set of ordered pairs?

Back

The domain can be found by listing all the unique x-values from the ordered pairs.