Functions and Inverse Function Vocabulary

The range of the inverse of f(x) = x³

( -∞ , ∞ )

One-to-one Function

A property of functions where the same value for y is never paired with two different values of x (the function passes the horizontal line test)

Relation

A set of ordered pairs.

Horizontal Line Test

A way to establish if a function is one-to-one when looking at a function's graph. Determines if the function is invertible.

Vertical Line Test

A way to establish that a relation is a function.

Reflection about the line y = x.

A way to graphically see if two functions are inverses of each other.

Domain Restriction

Omitting specific values from a relation's set of input values, commonly to ensure that a function's inverse is also a function.

Inverse Function

The function obtained by switching the x and y variables. If a function is named f, this can be written as f⁻¹

Domain

The set of all input values of a relation.

Range

The set of all output values of a relation.

Invertible

When the inverse of a function is also a function.

The domain of the inverse of f(x) = x²

[0 , ∞)