Function vs Nonfunction

Front

What is a function in mathematics?

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 a non-function?

Back

A non-function is a relation where at least one input is related to more than one output.

Front

What is the Vertical Line Test?

Back

The Vertical Line Test is a method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, then the graph is not a function.

Front

Can a vertical line intersect a function's graph more than once?

Back

No, if a vertical line intersects a graph more than once, the graph does not represent 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

Give an example of a function.

Back

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

Front

Give an example of a non-function.

Back

An example of a non-function is the relation defined by the equation x^2 + y^2 = 1, which relates some x-values to multiple y-values.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is related to exactly one input, meaning no two different inputs produce the same output.

Front

What is a many-to-one function?

Back

A many-to-one function is a function where multiple inputs can produce the same output.