Arithmetic Sequence

A sequence in which the difference between consecutive terms is constant

Asymptote

A line that a graph approaches more and more closely\

Change of Base formula

A formula used to change the base of a Logarithm

Circle

A shape with no corners or edges, typically measured through pi, or π

Combined Variation

the combination of direct and inverse proportionality. If a variable has a combined proportionality with two other variables, then it has a direct proportion with one and an inverse proportion with the other.

Common Difference

The costant difference d beween consecutive terms of an arithmetic sequence

Common Logarithm

A logarithm with base 10, denoted as log or log10

Common Ratio

The constant ratio r between consecutive terms of a geometric sequence

Completing the Square

To add a term c to an expression of the form x^2 +bx such that x^2 +bx + c is a perfect square trinomial

Complex Conjugates

Pairs of complex numbers of the forms a + bi and a-bi where b does not equal 0

Complex Fraction

A fraction that contains a fraction in its numerator o denominator

Complex Number

In mathematics, a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers

Composite of Functions

An operation that can be performed with two functions

Compound inequality

A compound inequality is an inequality that combines two simple inequalities.

Conic Section

a figure formed by the intersection of a plane and a right circular cone. Depending on the angle of the plane with respect to the cone, a conic section may be a circle, an ellipse, a parabola, or a hyperbola

Consistent

In mathematics and particularly in algebra, a linear or nonlinear system of equations is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system—that is, when substituted into each of the equations, they make each equation hold true as an identity.

Constant of Variation

The constant of variation in a direct variation is the constant (unchanged) ratio of two variable quantities. The formula for direct variation is. y=kx (or y=kx )

Continuous Relation

A set of data is said to be continuous if the values belonging to the set can take on ANY value within a finite or infinite interval.

Correlation Coefficient

a number between −1 and +1 calculated so as to represent the linear dependence of two variables or sets of data.

Dependent

The dependent variable is the one that depends on the value of some other number. If, say, y = x+3, then the value y can have depends on what the value of x is. Another way to put it is the dependent variable is the output value and the independent variable is the input value.

Dimensions of a Matrix

The dimensions of a matrix are the number of rows by the number of columns. If a matrix has a rows and b columns, it is an a×b matrix. For example, the first matrix shown below is a 2×2 matrix; the second one is a 1×4 matrix; and the third one is a 3×3 matrix.

Direct Variation

Direct variation describes a simple relationship between two variables . We say y varies directly with x (or as x , in some textbooks) if: y=kx. for some constant k , called the constant of variation or constant of proportionality .

Discriminant

In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and determines various properties of the roots. It is generally defined as a polynomial function of the coefficients of the original polynomial

Ellipse

In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. As such, it generalizes a circle, which is the special type of ellipse in which the two focal points are the same

End Behavior

The end behavior of a function f describes the behavior of the graph of the function at the “ends” of the x-axis. In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).

Exponential Equation

equations is which variable expressions occur as exponents

Extraneous Solution

solutions that are not solutions of the original equation

Extrema

In mathematical analysis, the maxima and minima of a function, known collectively as extrema, are the largest and smallest value of the function, either within a given range, or on the entire domain.

Factor Theorem

In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial f(x) has a factor if and only if f(k)=0

Finite Sequence

A sequence is finite if it has a limited number of terms and infinite if it does not. Finite sequence: {4,8,12,16,…, 64}

Function

In mathematics, a function is a binary relation between two sets that associates to each element of the first set exactly one element of the second set. Typical examples are functions from integers to integers, or from the real numbers to real numbers.

Geometric Sequence

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Greatest Integer Function

The greatest integer function is a function that returns a constant value for each specific interval. These functions are normally represented by an open and closed bracket, [ ]. These values are the rounded-down integer values of the expression found inside the brackets.

Growth Factor

The value of b in an exponential growth function of the form y=ab^x, where a > 0 and b > 1

Hyperbola

In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

Identity function

In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument. That is, for f being identity, the equality f(x) = x holds for all x.

Imaginary Unit

The square root of -1, denoted i = the square root of -1

Inconsistent

When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

Independent

An independent variable is a variable that represents a quantity that is being manipulated in an experiment. A dependent variable represents a quantity whose value depends on those manipulations.

Infinite Sequence

An infinite sequence is a list or string of discrete objects, usually numbers, that can be paired off one-to-one with the set of positive integer s {1, 2, 3, …}. … An infinite series is the sum of the values in an infinite sequence of numbers.

Interval Notation

Interval notation is a way of writing subsets of the real number line . A closed interval is one that includes its endpoints: for example, the set {x | −3≤x≤1} . An open interval is one that does not include its endpoints, for example, {x | −3

Inverse Function

functions that undo each other

Inverse Relation

An inverse relation is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function. If the graph of a function contains a point (a, b), then the graph of the inverse relation of this function contains the point (b, a).

Inverse Variation

mathematical relationship between two variables which can be expressed by an equation in which the product of two variables is equal to a constant

Joint Variation

Joint variation describes a situation where one variable depends on two (or more) other variables, and varies directly as each of them when the others are held constant. We say z varies jointly as x and y if. z=kxy. for some constant k.

Latus Rectum

The latus rectum of a conic section is the chord through a focus parallel to the conic section directrix (Coxeter 1969). “Latus rectum” is a compound of the Latin latus, meaning “side,” and rectum, meaning “straight.”

Linear Programming

a mathematical technique for maximizing or minimizing a linear function of several variables, such as output or cost.

Logarithm

a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.

Logistic Growth Model

In logistic growth, a population’s per capita growth rate gets smaller and smaller as population size approaches a maximum imposed by limited resources in the environment, known as the carrying capacity (K).

Matrix

a rectangular array of quantities or expressions in rows and columns that is treated as a single entity and manipulated according to particular rules.

nth Root

In mathematics, an nth root of a number x is a number r which, when raised to the power n, yields x: {\displaystyle r^{n}=x, } where n is a positive integer, sometimes called the degree of the root. A root of degree 2 is called a square root and a root of degree 3, a cube root.

Natural Logarithm

The natural logarithm of a number is its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately equal to 2.718281828459

Negative Exponent

A negative exponent means how many times to divide by the number. Example: 8-1 = 1 ÷ 8 = 1/8 = 0.125. Or many divides: Example: 5-3 = 1 ÷ 5 ÷ 5 ÷ 5 = 0.008.

Parabola

a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.

Parent Function

In mathematics, a parent function is the simplest function of a family of functions that preserves the definition of the entire family. For example, for the family of quadratic functions having the general form y=ax^{2}+bx+c\, the simplest function is y=x^{2}

Piece-wise defined function

In mathematics, a piecewise-defined function is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain. Piecewise definition is actually a way of expressing the function, rather than a characteristic of the function itself.

Point-Slope Form

a formula used to determine a slope of a function based on the coordinates of two points along a function, the formula is notated as y − y1 = m(x − x1)

Quadratic Function

In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree.

Radicand

the symbol in which numbers to the nth root reside

Rate of Change

The rate of change (ROC) is the speed at which a variable changes over a specific period of time.

Rational Exponent

A rational exponent is an exponent that is a fraction

Rational Function

In mathematics, a rational function is any function which can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K.

Rationalizing the Denominator

To rationalize the denominator means to eliminate any radical expressions in the denominator such as square roots and cube roots. The key idea is to multiply the original fraction by an appropriate value, such that after simplification, the denominator no longer contains radicals.

Recursive Formula

A recursive formula is a formula that defines each term of a sequence using preceding term(s). Recursive formulas must always state the initial term, or terms, of the sequence.

Regression line

In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables.

Relative Maximum

A relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a “peak” in the graph). Similarly, a relative minimum point is a point where the function changes direction from decreasing to increasing (making that point a “bottom” in the graph).

Relative Minimum

A relative minimum of a function is all the points x, in the domain of the function, such that it is the smallest value for some neighborhood. These are points in which the first derivative is 0 or it does not exist.

Root

A solution of an equation

Scatter Plot

a graph in which the values of two variables are plotted along two axes, the pattern of the resulting points revealing any correlation present.

Sequence

An ordered list of numbers

Set-Builder Notation

Uses symbols to define a set, in terms of the properties of the members of the set.

Step Function

A piece-wise function defined by a constant value over each part of its domain

synthetic division

A shortcut method to divide a polynomial by a binomial of the form x-k

vertex form

A quadratic function written in the form f(x)=a(x-h)²+k, where a does not equal 0

vertical line test

when determining if a line is a funtion, you run a vertical line across the line and if two or more lines are touching the vertical line at one time, it is not a function

zeroes

an x-value of a function f fro which f(x)=0