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 that corresponds to more than one output.

Front

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

Back

The function f(x) = x^2 is a function but not one-to-one because both f(2) and f(-2) yield the same output (4).

Front

What is the definition of a domain in 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 definition of a range in a function?

Back

The range of a function is the set of all possible output values (y) that the function can produce.

Front

What is the difference between a function and a relation?

Back

All functions are relations, but not all relations are functions. A function has a unique output for each input.

Front

What is an example of a one-to-one function?

Back

The function f(x) = 2x + 3 is one-to-one because each input produces a unique output.