Identifying functions

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

What does it mean if x-values repeat in a mapping?

Back

If x-values repeat in a mapping, it is not a function because a single input cannot correspond to multiple outputs.

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

How can you tell if a graph is a function?

Back

A graph is a function if it passes the vertical line test, meaning no vertical line intersects the graph at more than one point.

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 that function.

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 result from the function.

Front

Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input; this would violate the definition of a function.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value corresponds to one unique y-value.

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 corresponds to two different outputs.

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.