Functions Flashcard

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

What is the vertical line test?

Back

The vertical line test is a method 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

A relation is a function if every input (x-value) has exactly one output (y-value).

Front

Give an example of a function.

Back

An example of a function is f(x) = 2x + 3, where each x-value corresponds to one y-value.

Front

What is a mapping in mathematics?

Back

A mapping is a way to describe how each element of one set (domain) is paired with an element of another set (range).

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 that function.

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

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one 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 related to two different outputs.

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.