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 identify a function from a set of ordered pairs?

Back

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

Front

What does it mean for y to be a function of x?

Back

It means that for every value of x, there is exactly one corresponding value of y.

Front

What is the vertical line test?

Back

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

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 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 difference between a function and a relation?

Back

A relation is any set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.

Front

How can you tell if a table represents y as a function of x?

Back

A table represents y as a function of x if each x-value is unique and corresponds to only one y-value.

Front

What does it mean if a graph does not represent a function?

Back

It means that there exists at least one x-value that corresponds to more than one y-value.

Front

What is an example of a function?

Back

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