Identifying Functions

Front

What is a function in mathematical terms?

Back

A function is a relation that assigns exactly one output for each input.

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What does it mean for a relation to not be a function?

Back

A relation is not a function if at least one input is associated with more than one output.

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 intersects the graph more than once.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents the relationship between inputs and outputs, showing how each input is paired with an output.

Front

What is the definition of 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 map to the same output.

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 function is a specific type of relation where each input is related to exactly one output, while a relation can have multiple outputs for a single input.

Front

What is an example of a function?

Back

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

Front

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

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input 1 is associated with two different outputs.