Radical Functions Vocabulary

Radical Functions and Rational Exponents Vocabulary

• nth root: Represents a number 'a' such that when raised to the power of 'n', it equals 'b'; defines the relationship between 'a' and 'b' using exponentiation.

• principal root: Specifically refers to the positive square root of a given number, distinguishing it from negative roots.

• Radicand: The term for the value or expression located beneath the radical symbol, crucial for understanding radical functions.

• index of a root: Indicates the degree of the root being taken; for instance, an index of 2 signifies a square root.

• simplest form of a radical: Achieved when the radicand contains no factors that are perfect nth powers, and all denominators in radicals are rationalized.

• rationalize the denominator: Process of transforming a fraction to eliminate radicals from the denominator and ensuring that no fractional terms exist within any radical.

• like radicals: Refers to radical expressions that share both the same index and the same radicand, allowing for the possibility of combining them.

• rational exponent: Indicates a relationship where if the nth root of 'a' is real, and 'm/n' (where 'm' is an integer) is expressed in its simplest form, the rules of rational exponents apply.

• radical equation: A type of equation that incorporates a variable within a radicand or involves a variable that possesses a rational exponent.

• square root equation: A specific category of radical equation characterized by having a square root, thus an index of 2.

• composite function: Formed when the output from one function is fed as input into another function, resulting in a new function.

• inverse relation: Represents a relationship where each element 'a' from the domain corresponds to an element 'b' in the range, and vice versa for the inverse.

• inverse function: When a relation and its inverse qualify as functions, they are denoted as inverse functions, illustrating a unique correspondence between inputs and outputs.

• one-to-one function: Ensures that each output in the range is associated with one and only one input from the domain, establishing a bijective relation.

• radical function: Encompasses any function that integrates a radical expression with a variable present within the radicand.

• square root function: A specific type of radical function that features the square root of a variable as its primary operation.