Relations: Domain, Range, & Functions

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 which the function is defined.

Front

What is the range of a function?

Back

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

Front

How can you determine if a relation is a function?

Back

A relation is a function if each input value (x) is associated with exactly one output value (y).

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

Given the relation {(1, 2), (1, 3), (2, 4)}, is it a function?

Back

No, it is not a function because the input value 1 is associated with two different output values (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 value is associated with exactly one input value.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents the relationship between the domain and range of a function.

Front

If a function has 5 ordered pairs, how many outputs can it have?

Back

It can have up to 5 outputs, but it may have fewer if some inputs share the same output.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function; if a vertical line intersects the curve at more than one point, it is not a function.

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 has exactly one output.