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

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a coordinate system, typically written as (x, y).

Front

What does it mean for a set of ordered pairs to be a function?

Back

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

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If any vertical line intersects the graph more than once, it is not a function.

Front

Give an example of a function using ordered pairs.

Back

Example: {(1, 2), (2, 3), (3, 4)} is a function because each input (1, 2, 3) has a unique output (2, 3, 4).

Front

Give an example of a relation that is not a function.

Back

Example: {(1, 2), (1, 3)} is not a function because the input 1 is associated with two different outputs (2 and 3).

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 tell if a graph is a function?

Back

You can tell if a graph is a function by using the vertical line test.

Front

What does it mean if a graph fails the vertical line test?

Back

If a graph fails the vertical line test, it means that there are at least two points on the graph that have the same x-coordinate, indicating it is not a function.