Algebra II deck 2 Flashcards
Zeros
the values of x when f(x) is equal to 0
vertical line test
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.
Vertex form
a point where two or more curves, lines, or edges meet.
Synthetic division
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.
step function
a piecewise-defined function in which every piece is a horizontal line segment or a point.
Set-builder notation
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}
Sequence
ordered lists of numbers (called “terms”)
Root
a solution to an equation, usually expressed as a number or an algebraic formula.
nth root
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.
nth root
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.
relative minimum
all the points x, in the domain of the function, such that it is the smallest value for some neighborhood.
Relative maximum
a point where the function changes direction from increasing to decreasing
Regression line
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)
Recursive formula
a formula that defines each term of a sequence using preceding term(s)
Rationalizing the denominator
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).
Rational function
A function that is the ratio of two polynomials
rational exponent
expressions with exponents that are rational numbers
Rate of change
Rate of change is used to mathematically describe the percentage change in value over a defined period of time
Radicand
The number or expression whose square root or other root is being considered
Quadratic function
f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.
Point-slope 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
Piece-wise defined function
A piecewise-defined function is a function whose domain is divided into parts and each part is defined by a different function rule.
Parent function
the simplest function that still satisfies the definition of a certain type of function.
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.
Negative exponent
the multiplicative inverse of the base, raised to the power which is opposite to the given power.
Natural logarithm
logarithm to the base of the mathematical constant e
nth root
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.
matrix
matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns
Logistic growth model
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.
Logarithm
a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
linear programming
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.
Latus rectum
a chord of a conic section (such as an ellipse) that passes through a focus and is parallel to the directrix.
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.
Inverse variation
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.
Inverse relation
a set of ordered pairs which are obtained by interchanging the first and second elements of the ordered pairs of the given relation.
Interval notation
a way of writing subsets of the real number line
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
Independent
A variable in an equation that may have its value freely chosen without considering values of any other variable.
Inconsistent
if there is no solution because the lines are parallel
Imaginary unit
An imaginary number is a real number multiplied by the imaginary unit i, which is defined by its property i2 = −1.
Identity function
assigns every real number to the same real number
Hyperbola
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.
Growth factor
a naturally occurring substance capable of stimulating cell proliferation, wound healing, and occasionally cellular differentiation.
Greatest Integer Function
a function that gives the largest integer which is less than or equal to x.
Geometric sequence
a sequence in which each term is found by multiplying the preceding term by the same value.
Function
an equation that has only one answer for y for every x.
Finite sequence
a grouping of numbers in a specific order with a clear starting point and stopping point.
Factor Theorem
usually used to factor and find the roots of polynomials.
Extrema
any point at which the value of a function is largest (a maximum) or smallest (a minimum)
Extraneous solution
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
Exponential equation
f(x) = ax
End behavior
the end behavior of a function describes the trend of the graph if we look to the right end
Ellipse
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.
Discriminant
b²-4ac
Direct variation
y = kx, k ≠ 0.
Dimensions of a matrix
the number of rows by the number of columns
dependent
The variable whose value depends on the other variable is the dependent variable.
Correlation coefficient
measures the direction and strength of a linear relations
Continuous relation
if it is upper hemicontinuous and lower hemicontinuous.
Constant of variation
The ratio between two variables in a direct variation or the product of two variables in an inverse variation
Consistent
if there is at least one set of values for the unknowns that satisfies each equation in the system
Conic section
a curve obtained as the intersection of the surface of a cone with a plane
Compound inequality
a sentence with two inequality statements joined either by the word “or” or by the word “and.”
Composition of functions
It combines two or more functions to result in another function.
Complex number
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”
Complex Fraction
a fraction in which the denominator and numerator or both contain fractions
Complex conjugates
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.
Completing the square
ax2 + bx + c ⇒ (x + p)2 + constant
Common ratio
the amount between each number in a geometric sequence.
Common logarithm
common logarithm is the logarithm with base 10
Common difference
the difference between two consecutive terms of an arithmetic progression.
Combined variation
a situation where a variable depends on two (or more) other variables, and varies directly with some of them and varies inversely with others
Circle
a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).
Change of base formula
logb b a = [logc c a] / [logc c b]
Asymptote
a line that continually approaches a given curve but does not meet it at any finite distance.
Arithmetic sequence
a sequence where each term increases by adding/subtracting some constant k.
