01-03 Relations, Functions, One-to-One Functions

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x) and an output (y).

Front

What is a function?

Back

A function is a special type of relation where each input (x) is associated with exactly one output (y).

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output (y) is associated with exactly one input (x), meaning no two different inputs produce the same output.

Front

How can you determine if a relation is a function using the vertical line test?

Back

If a vertical line intersects the graph of the relation at more than one point, then the relation is not a function.

Front

What does it mean for a function to be 'not a function'?

Back

It means that there exists at least one input (x) that is associated with more than one output (y).

Front

What is the difference between a function and a one-to-one function?

Back

All one-to-one functions are functions, but not all functions are one-to-one. A function can have multiple inputs mapping to the same output.

Front

Provide an example of a one-to-one function.

Back

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

Front

Provide an example of a function that is not one-to-one.

Back

An example of a function that is not one-to-one is f(x) = x^2, where both x = 2 and x = -2 produce the same output.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x) 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) that the function can produce.