Chapter 5 Vocabulary Algebra 2

• index

• base

• exponent

• coefficient

nth root of a

• The value of b such that bⁿ = a

• The value of a such that aⁿ = b

• The value of n such that n^b = a

• The value of a when n is equal to 1

Inverse functions

• Functions that undo each other.

• Functions that are always increasing.

• Functions that have the same output for different inputs.

• Functions that are defined only for positive numbers.

Radical function

• A function that contains a radical expression with the independent variable in the radicand.

• A function that is defined only for positive values of the independent variable.

• A function that has a constant rate of change.

• A function that can be expressed as a polynomial of degree one.

Simplest form of a radical

• An expression involving a radical with an index n that has no radicands with perfect nth powers as factors other than 1, no radicans that contain fractions, and no radicals that appear in the denominator of a fraction.

• A radical expression that contains only integers and no variables.

• A radical expression that has been simplified to its lowest terms, including all possible factors.

• A radical expression that includes fractions and perfect squares.

Square root function

• A function that contains a square root with the independent variable in the radicand.

• A function that only contains positive integers.

• A function that is defined for all real numbers.

• A function that has a constant output regardless of the input.

Like radicals

• Radical expressions with different indices and radicands.

• Radical expressions with the same index and radicand.

• Radical expressions that are not similar.

• Radical expressions that can be simplified to integers.

Index of a radical

• The value of n in the radical @@\sqrt[n]{a}@@.

• The base of the radical @@\sqrt[n]{a}@@.

• The exponent of the radical @@\sqrt[n]{a}@@.

• The coefficient of the radical @@\sqrt[n]{a}@@.

Composition

• A method of combining two or more functions where the output of one function is used as the input of another function.

• A process of adding two functions together to create a new function.

• A technique for differentiating functions to find their rates of change.

• A way to graph functions on a coordinate plane.

Cube root function

• A linear function with an index of 1.

• A quadratic function with an index of 2.

• A radical function with an index of 3.

• An exponential function with a base of e.