Flashcards in Finals Deck (75)

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1

## Arithmetic Sequence

### A sequence in which the difference of consecutive terms in constant

2

## Asymptote

### An line that a graph approaches more and more closely

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## Change of base formula

### A formula that allows you to rewrite logarithms in terms with another base.

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## Circle

### Consists of all points in a plane, that are a given distance from a given point.

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## Combined variation

### Describes a situation where a variable depends on two other variables, and varies directly with some of them and varies inversely with others.

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## Common difference

### The constant difference d between consecutive terms of an arithmetic sequence.

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## Common logarithm

### A logarithm with base 10, denoted by log.

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## Common ratio

### The constant ratio r between consecutive terms of geometric sequence.

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## Completing the square

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

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## Complex conjugates

### Pairs of complex numbers of the forms a+bi and a-bi, where x cannot =0

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## Complex fraction

### A fraction that contains a fraction in its numerator and denominator.

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## Complex number

### A number written in the form a+bi, where a and b are real numbers.

13

## Composition of fractions

### A function that takes up operations, that uses g and f.

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## Compound inequality

### Is a compound that combines two simple inequalities.

15

## Conic Section

### A figure formed by intersection of a plane and a right circular cone.

16

## Consistent

### A linear on non linear system of equations. if there is one value that satisfies the equation.

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## Constant of variation

### The constant a in the inverse variation is on bottom

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## Continuos 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. Definition: A set of data is said to be discrete if the values belonging to the set are distinct and separate (unconnected values).

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## Correlation coefficient

### A number that is a measure of the strength and direction of the correlation between two variables.

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## 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. An

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## Diminsions 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.

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## 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 .

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## 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

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## Ellipse

### 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.

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## End behavior

### of a graph is defined as what is going on at the ends of each graph. ... As the function approaches positive or negative infinity, the leading term determines what the graph looks like as it moves towards infinity.

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## Exponential equation

### are equations in which variables occur as exponents. For example, exponential equations are in the form ax=by . To solve exponential equations with same base, use the property of equality of exponential functions . ... In other words, if the bases are the same, then the exponents must be equal.

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## Extraneous solution

### are values that we get when solving equations that aren't really solutions to the equation.

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## Extrema

### the maxima and minima of a function,

29

## Factor theorem

### is used when factoring polynomials "completely". ... Any time you divide by a number (being a potential root of the polynomial) and get a zero remainder in the synthetic division, this means that the number is indeed a root, and thus "x minus the number" is a factor.

30

## finite sequence

### is a list of terms in a specific order. The sequence has a first term and a last term.

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## function

### a relationship or expression involving one or more variables

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## 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.

33

## greatest integer function

### , also called step function, is a piecewise function whose graph looks like the steps of a staircase. The greatest integer function is denoted by f(x) = [x] and is defined as the greatest integer less or equal to x. Example #1. [2.5] is the greatest integer less or equal to 2.5.

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## growth factor

### is the factor by which a quantity multiplies itself over time

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## 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.

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## identity function

### is a function that always returns the same value that was used as its argument.

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## imaginary unit

### is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i² = −1. The square of an imaginary number bi is −b². For example, 5i is an imaginary number, and its square is −25. Wikipedia

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## inconsistent

### is the study of commonplace mathematical objects, like sets, numbers, and functions, where some contradictions are allowed. ...

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## independent

### 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.

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## infinite sequence

### s 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, .

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## interval notation

### is a way to describe continuous sets of real numbers by the numbers that bound them. Intervals, when written, look somewhat like ordered pairs. However, they are not meant to denote a specific point. Rather, they are meant to be a shorthand way to write an inequality or system of inequalities.

42

## inverse function

### s a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, i.e., g(y) = x if and only if f(x) = y. The inverse function of f is also denoted as f^{-1}. Wikipedia

43

## inverse relation

### is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function.

44

## 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.

45

## joint variation

### occurs when a variable varies directly or inversely with multiple variables. For instance, if x varies directly with both y and z, we have x = kyz.

46

## 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."

47

## linear programming

### is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming.

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## logarithm

### is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.

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## logistic growth model

### is a common S-shaped curve with equation {\displaystyle f(x)={\frac {L}{1+e^{-k}}}, } where x_{0}, the x value of the sigmoid's midpoint; L, the curve's maximum value; k, the logistic growth rate or steepness of the curve

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## matrix

### is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. For example, the dimension of the matrix below is 2 × 3, because there are two rows and three columns: {\displaystyle

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## n^th 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. Wikipedia

52

## natural logarithm

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

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## negative exponent

### how many times to divide by the number.

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## parabola

### s a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point and a line.

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## 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

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## piece wise 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. Wikipedia

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## point slope form

### the equation of a straight line in the form y − y1 = m(x − x1) where m is the slope of the line and (x1, y1) are the coordinates of a given point on the line — compare slope-intercept form.

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## 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. Wikipedia

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## radicand

### 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.

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## rate of change

### is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable.

61

## rational exponent

### is an exponent that is a fraction. For example, can be written as . ... Let's explore the relationship between rational (fractional) exponents and radicals.

62

## rationalizing 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.

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## recursive formula

### is a formula that defines each term of a sequence using preceding term(s).

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## regression line

### is an estimate of the line that describes the true, but unknown, linear relationship between the two variables.

65

## relative minimum

### 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.

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## relative maximum

### point is a point where the function changes direction from increasing to decreasing (making that point a "peak" in the graph)

67

## root

### a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4² = ² = 16.

68

## scatter plot

### chart, scattergram, or scatter diagram) is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.

69

## sequence

### is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members. The number of elements is called the length of the sequence. Wikipedia

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## set builder notation

### is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy. Usually with infinite number sets.

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## step function

### a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals. Informally speaking, a step function is a piecewise constant function having only finitely many pieces.

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## synthetic division

### is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division. It is mostly taught for division by linear monic polynomials, but the method can be generalized to division by any polynomial.

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## vertex form

### is a point where two or more curves, lines, or edges meet. ... Vertex is also sometimes used to indicate the 'top' or high point of something, such as the vertex of an isosceles triangle, which is the 'top' corner opposite its base, but this is not its strict mathematical definition

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## vertical line test

### is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x. Wikipedia

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