Functions and Relations

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from a given set.

Front

What is the definition of a relation?

Back

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

Front

How can you determine if a mapping is a function?

Back

A mapping is a function if every input is associated with exactly one output.

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 intersects the graph at more than one point, it is not a function.

Front

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

Back

A mapping is 'not a function' if at least one input is associated with more than one output.

Front

What is an example of a function?

Back

An example of a function is f(x) = x^2, where each input x has a unique 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 the set {(1, 2), (1, 3)}, where the input 1 is associated with two different outputs.

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 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-values) that the function can produce.

Front

What is a one-to-one function?

Back

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