Is it a Function?

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 the vertical line test?

Back

The vertical line test is a method used to determine if a curve is a function. If a vertical line intersects the curve at more than one point, then the curve is not a function.

Front

What does it mean for a relation to be a function?

Back

For a relation to be a function, each input must correspond to exactly one output.

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 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 non-function?

Back

An example of a non-function is the relation defined by the equation y^2 = x, as it produces two outputs (y values) for some inputs (x values).

Front

What is a one-to-one function?

Back

A one-to-one function is a function in which each output is associated with exactly one input, meaning no two different inputs produce the same output.

Front

What is an example of a function?

Back

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

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input is associated with exactly one output, while a relation can have multiple outputs for a single input.