Algebra 2 Final Exam Study Guide Vocabulary

This set of vocabulary flashcards covers essential algebraic concepts from the Version D Algebra 2 Final Exam Study Guide, including radicals, rational functions, sequences, matrices, logarithms, and trigonometry.

Simplest Radical Form

The form of an expression where the radicand contains no perfect square factors (other than $1$) and no radicals remain in the denominator.

Rational Denominator

The process of simplifying an expression such that the denominator contains no radical symbols.

Undefined Rational Expression

A state that occurs when the denominator of a rational expression is equal to $0$.

Vertical Asymptote

A vertical line on a graph that the function approaches but never touches, occurring where the denominator of a simplified rational function equals $0$.

Hole (in a graph)

A point on the graph of a rational function where both the numerator and the denominator are zero for the same value of $x$.

Slant Asymptote

A linear asymptote that is neither horizontal nor vertical, found in rational functions where the degree of the numerator is exactly one greater than the degree of the denominator.

Exponential Growth

A function in the form $y = ab^x$ where the base $b > 1$, representing an increase at a constant percentage rate.

Exponential Decay

A function in the form $y = ab^x$ where the base $0 < b < 1$, representing a decrease at a constant percentage rate.

Arithmetic Sequence

A sequence of numbers where the difference between consecutive terms is constant.

Geometric Sequence

A sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Explicit Formula

A formula that allows for the calculation of any term in a sequence ($a_n$) based on its position $n$.

$f^{-1}(x)$ (Inverse Function)

A function that reverses the operation of the original function $f(x)$, such that the domain and range are swapped.

Logarithmic Equation

An equation involving a logarithm, which is the inverse operation of exponentiation, such as $\text{log}_b(y) = x$.

Change of Base Formula

A formula used to evaluate logarithms with any base, typically expressed as $\text{log}_b(a) = \frac{\text{log}_c(a)}{\text{log}_c(b)}$.

Element $a_{ij}$

The value located in the $i\text{-th}$ row and $j\text{-th}$ column of a matrix.

Order of a Matrix

The dimensions of a matrix, expressed as $m \times n$, where $m$ is the number of rows and $n$ is the number of columns.

Determinant

A scalar value derived from a square matrix that can be used to solve systems of linear equations or find the area of geometric figures.

Cramer’s Rule

A method for solving a system of linear equations using the determinants of the coefficient matrix and related matrices.

Radian

A unit of angular measure where the total measure of a circle is 2\text{\textpi} radians, equivalent to $360^{\circ}$.

Unit Circle Trig Ratios

Definitions of trigonometric functions based on a circle with radius $1$, where $\text{sin}(\theta) = y$, $\text{cos}(\theta) = x$, and $\text{tan}(\theta) = \frac{y}{x}$.