Functions vs Relations

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 specific type of relation where each input (x) is associated with exactly one output (y).

Front

What does 'one-to-many' mean in the context of relations?

Back

'One-to-many' means that a single input (x) can be associated with multiple outputs (y), which indicates that it is not a function.

Front

What does 'many-to-one' mean in the context of functions?

Back

'Many-to-one' means that multiple inputs (x) can be associated with the same output (y), which is acceptable in functions.

Front

How can you determine if a relation is a function using a graph?

Back

A relation is a function if any vertical line drawn on the graph intersects the curve at most once (Vertical Line Test).

Front

What is the Vertical Line Test?

Back

The Vertical Line Test is a method to determine if a graph represents a function; if a vertical line crosses the graph more than once, it is not a function.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point in a coordinate system.

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.

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 corresponds to only one output.