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 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 a mapping in the context of functions?

Back

A mapping shows how each element of one set (domain) is paired with an element of another set (range).

Front

Can a function have two different outputs for the same input?

Back

No, a function cannot have two different outputs for the same input; this would violate the definition of a function.

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

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.

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 is paired with two different outputs.

Front

What is the importance of the Vertical Line Test?

Back

The Vertical Line Test is important because it helps determine if a graph represents a function.