Identifying 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

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 are ordered pairs in the context of functions?

Back

Ordered pairs are pairs of numbers (x, y) that represent coordinates on a graph, where 'x' is the input and 'y' is the output.

Front

What does it mean for ordered pairs to represent a function?

Back

Ordered pairs represent a function if each unique input (x-value) corresponds to exactly one output (y-value).

Front

What is a mapping in mathematics?

Back

A mapping is a way to show how each element from one set (domain) is paired with an element from another set (range).

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, but each input must have only 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 crosses the graph more than once.

Front

What is the difference between a function and a relation?

Back

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

Front

Give an example of a function using ordered pairs.

Back

Example: {(1, 2), (2, 3), (3, 4)} is a function because each x-value is unique.

Front

Give an example of a relation that is not a function using ordered pairs.

Back

Example: {(1, 2), (1, 3), (2, 4)} is not a function because the input '1' has two different outputs.