Identifying Functions

Front

What is a function in mathematics?

Back

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

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-values) 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-values) that the function can produce.

Front

How can you determine if a relation is a function?

Back

A relation 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 curve is a function; if a vertical line intersects the curve at more than one point, it is not a function.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, 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 of points {(1,2), (1,3)}, where the input 1 is associated with two different outputs.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it assigns a unique output for every unique input, meaning no two different inputs produce the same output.

Front

What is a composite function?

Back

A composite function is formed when one function is applied to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

What is an inverse function?

Back

An inverse function reverses the effect of the original function, denoted as f^(-1)(x), such that f(f^(-1)(x)) = x.