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Algebra II Final > Algebra II deck 2 > Flashcards

Algebra II deck 2 Flashcards

1
Q

Zeros

A

the values of x when f(x) is equal to 0

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2
Q

vertical line test

A

a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.

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3
Q

Vertex form

A

a point where two or more curves, lines, or edges meet.

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4
Q

Synthetic division

A

Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor – and it only works in this case. Synthetic division is generally used, however, not for dividing out factors but for finding zeroes (or roots) of polynomials.

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5
Q

step function

A

a piecewise-defined function in which every piece is a horizontal line segment or a point.

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6
Q

Set-builder notation

A

mathematical notation for describing a set by representing its elements or explaining the properties that its members must satisfy. For example, C = {2,4,5}

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7
Q

Sequence

A

ordered lists of numbers (called “terms”)

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8
Q

Root

A

a solution to an equation, usually expressed as a number or an algebraic formula.

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9
Q

nth root

A

a number r which, when raised to the power n, yields x: where n is a positive integer, sometimes called the degree of the root.

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10
Q

nth root

A

a number r which, when raised to the power n, yields x: where n is a positive integer, sometimes called the degree of the root.

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11
Q

relative minimum

A

all the points x, in the domain of the function, such that it is the smallest value for some neighborhood.

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12
Q

Relative maximum

A

a point where the function changes direction from increasing to decreasing

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13
Q

Regression line

A

A regression line is simply a single line that best fits the data (in terms of having the smallest overall distance from the line to the points)

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14
Q

Recursive formula

A

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

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15
Q

Rationalizing the denominator

A

the process of moving a root, for instance, a cube root or a square root from the bottom of a fraction (denominator) to the top of the fraction (numerator).

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16
Q

Rational function

A

A function that is the ratio of two polynomials

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17
Q

rational exponent

A

expressions with exponents that are rational numbers

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18
Q

Rate of change

A

Rate of change is used to mathematically describe the percentage change in value over a defined period of time

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19
Q

Radicand

A

The number or expression whose square root or other root is being considered

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20
Q

Quadratic function

A

f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.

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21
Q

Point-slope form

A

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

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22
Q

Piece-wise defined function

A

A piecewise-defined function is a function whose domain is divided into parts and each part is defined by a different function rule.

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23
Q

Parent function

A

the simplest function that still satisfies the definition of a certain type of function.

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24
Q

Parabola

A

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.

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25
Q

Negative exponent

A

the multiplicative inverse of the base, raised to the power which is opposite to the given power.

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26
Q

Natural logarithm

A

logarithm to the base of the mathematical constant e

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27
Q

nth root

A

a number r which, when raised to the power n, yields x: where n is a positive integer, sometimes called the degree of the root.

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28
Q

matrix

A

matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns

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29
Q

Logistic growth model

A

ogistic growth is population increase that happens in a manner that starts slowly, as there are few individuals, then increases in speed as numbers increase, but then decreases to a halt as numbers get high enough that resources are depleted and cannot support further growth.

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30
Q

Logarithm

A

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

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31
Q

linear programming

A

a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.

32
Q

Latus rectum

A

a chord of a conic section (such as an ellipse) that passes through a focus and is parallel to the directrix.

33
Q

Joint variation

A

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.

34
Q

Inverse variation

A

a nonlinear function defined by an equation of the form xy = k when x is not equal to zero and k is a nonzero real number constant.

35
Q

Inverse relation

A

a set of ordered pairs which are obtained by interchanging the first and second elements of the ordered pairs of the given relation.

36
Q

Interval notation

A

a way of writing subsets of the real number line

37
Q

Infinite sequence

A

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

38
Q

Independent

A

A variable in an equation that may have its value freely chosen without considering values of any other variable.

39
Q

Inconsistent

A

if there is no solution because the lines are parallel

40
Q

Imaginary unit

A

An imaginary number is a real number multiplied by the imaginary unit i, which is defined by its property i2 = −1.

41
Q

Identity function

A

assigns every real number to the same real number

42
Q

Hyperbola

A

a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.

43
Q

Growth factor

A

a naturally occurring substance capable of stimulating cell proliferation, wound healing, and occasionally cellular differentiation.

44
Q

Greatest Integer Function

A

a function that gives the largest integer which is less than or equal to x.

45
Q

Geometric sequence

A

a sequence in which each term is found by multiplying the preceding term by the same value.

46
Q

Function

A

an equation that has only one answer for y for every x.

47
Q

Finite sequence

A

a grouping of numbers in a specific order with a clear starting point and stopping point.

48
Q

Factor Theorem

A

usually used to factor and find the roots of polynomials.

49
Q

Extrema

A

any point at which the value of a function is largest (a maximum) or smallest (a minimum)

50
Q

Extraneous solution

A

An extraneous solution is a root of a transformed equation that is not a root of the original equation because it was excluded from the domain

51
Q

Exponential equation

A

f(x) = ax

52
Q

End behavior

A

the end behavior of a function describes the trend of the graph if we look to the right end

53
Q

Ellipse

A

An ellipse is the set of all points on a plane whose distance from two fixed points F and G add up to a constant.

54
Q

Discriminant

A

b²-4ac

55
Q

Direct variation

A

y = kx, k ≠ 0.

56
Q

Dimensions of a matrix

A

the number of rows by the number of columns

57
Q

dependent

A

The variable whose value depends on the other variable is the dependent variable.

58
Q

Correlation coefficient

A

measures the direction and strength of a linear relations

59
Q

Continuous relation

A

if it is upper hemicontinuous and lower hemicontinuous.

60
Q

Constant of variation

A

The ratio between two variables in a direct variation or the product of two variables in an inverse variation

61
Q

Consistent

A

if there is at least one set of values for the unknowns that satisfies each equation in the system

62
Q

Conic section

A

a curve obtained as the intersection of the surface of a cone with a plane

63
Q

Compound inequality

A

a sentence with two inequality statements joined either by the word “or” or by the word “and.”

64
Q

Composition of functions

A

It combines two or more functions to result in another function.

65
Q

Complex number

A

the numbers that are expressed in the form of a+ib where, a,b are real numbers and ‘i’ is an imaginary number called “iota”

66
Q

Complex Fraction

A

a fraction in which the denominator and numerator or both contain fractions

67
Q

Complex conjugates

A

another complex number that has the same real part as the original complex number and the imaginary part has the same magnitude but opposite sign.

68
Q

Completing the square

A

ax2 + bx + c ⇒ (x + p)2 + constant

69
Q

Common ratio

A

the amount between each number in a geometric sequence.

70
Q

Common logarithm

A

common logarithm is the logarithm with base 10

71
Q

Common difference

A

the difference between two consecutive terms of an arithmetic progression.

72
Q

Combined variation

A

a situation where a variable depends on two (or more) other variables, and varies directly with some of them and varies inversely with others

73
Q

Circle

A

a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).

74
Q

Change of base formula

A

logb b a = [logc c a] / [logc c b]

75
Q

Asymptote

A

a line that continually approaches a given curve but does not meet it at any finite distance.

76
Q

Arithmetic sequence

A

a sequence where each term increases by adding/subtracting some constant k.

Algebra II Final (2 decks)

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