Radical Functions Vocabulary

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Questions and Answers

What is the nth root?

For any real numbers a and b, and any positive integer n, if a^n = b, then a is an nth root of b.

What is the principal root?

The positive square root of a number.

What is a radicand?

The number under the radical sign.

What does the index of a root represent?

The index gives the degree of the root. Signup and view all the answers

What is the simplest form of a radical?

A radical with index n is in simplest form if the radicand has no perfect nth powers as factors and any denominator has been rationalized. Signup and view all the answers

What does it mean to rationalize the denominator?

Rewrite it so there are no radicals in any denominator and no denominators in any radical. Signup and view all the answers

What are like radicals?

Radical expressions with the same index and radicand. Signup and view all the answers

What is a rational exponent?

If the nth root of 'a' is a real number, m is an integer, and m/n is in lowest terms, then the rational exponent theorem follows. Signup and view all the answers

What is a radical equation?

An equation that has a variable in a radicand or has a variable with a rational exponent. Signup and view all the answers

What is a square root equation?

A radical equation in which the radical has index 2. Signup and view all the answers

What is a composite function?

A combination of two functions such that the output from the first function becomes the input for the second function. Signup and view all the answers

What is an inverse relation?

If a relation pairs element a of its domain to element b of its range, the inverse relation pairs b with a. Signup and view all the answers

What is an inverse function?

If both a relation and its inverse happen to be functions, they are 'inverse functions.' Signup and view all the answers

What is a one-to-one function?

A function where each element of the range is paired with exactly one element of the domain. Signup and view all the answers

What is a radical function?

A function that contains a radical with a variable in its radicand. Signup and view all the answers

What is a square root function?

A function that contains a square root of a variable. Signup and view all the answers

Study Notes

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.

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Description

Test your understanding of key terms related to radical functions and rational exponents. This quiz covers essential vocabulary including nth roots, principal roots, radicands, and simplifying radicals. Perfect for students studying algebra and preparing for exams.