Identifying Functions

Front

What is a function in mathematics?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the definition of a set of ordered pairs?

Back

A set of ordered pairs is a collection of pairs of elements, typically represented as (x, y), where 'x' is the input and 'y' is the output.

Front

How can you determine if a set of ordered pairs is a function?

Back

A set of ordered pairs is a function if no two pairs have the same first element (input) with different second elements (outputs).

Front

What does it mean for a mapping to represent a function?

Back

A mapping represents a function if each input is associated with exactly one output.

Front

What is an example of a set that is not a function?

Back

An example of a set that is not a function is {(2,3), (2,5), (4,9)} because the input '2' is associated with two different outputs.

Front

What is the significance of the vertical line test?

Back

The vertical line test is a method used to determine if a curve is a function; if any vertical line intersects the curve 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 corresponds to only one output.

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

What is a one-to-one function?

Back

A one-to-one function is a function where each output is associated with exactly one input, meaning no two different inputs produce the same output.