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 does it mean for a mapping to be a function?

Back

A mapping is a function if each input (domain) is paired with exactly one output (range).

Front

What is the Vertical Line Test?

Back

The Vertical Line Test is a method to determine if a curve is a graph of a function by checking if a vertical line intersects the graph more than once.

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 domain in 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 a range in a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Does the following mapping represent a function? {(1, 2), (1, 3), (2, 4)}

Back

No, because the input '1' is associated with two different outputs (2 and 3).

Front

Does the following table represent a function? x | y ---|--- 1 | 2 2 | 3 3 | 4

Back

Yes, each input (x) has exactly one output (y).

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.