Function vs. Relation

Front

What is a relation?

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 every input corresponds to exactly one output.

Front

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

Back

A mapping is a function if each input has one and only one output.

Front

What is the difference between a function and a relation?

Back

All functions are relations, but not all relations are functions. Functions have a unique output for each input.

Front

What is the domain of a function?

Back

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

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

How can you determine if a graph represents a function?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is an example of a non-function relation?

Back

A relation where an input has multiple outputs, such as the relation {(1, 2), (1, 3)}, is not a function.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is paired with 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.