Functions

Front

What is a function?

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 domain of a function?

Back

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

Front

What is the range of a function?

Back

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

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 (x-value).

Front

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

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once.

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, which can include functions but does not have the restriction of unique outputs for each input.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each input x has a unique output.

Front

What is an example of a non-function?

Back

An example of a non-function is the relation {(1, 2), (1, 3)}, where the input 1 has two different outputs.

Front

What is a one-to-one function?

Back

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