Algebra II terms Flashcards
A sequence in which the difference of consecutive terms is constant
Arithmetic sequence
A line that a graph approaches more and more closely
Asymptote
Log base a is equal to log base d of a divided by log base d of b
Change of base formula
A shape with no edges and points are equidistant
Circle
A variable depends on two or more other variables
Combined variation
The constant difference between consecutive terms of an arithmetic sequence
Common difference
a logarithm to the base 10.
Common logarithm
the ratio between a term and the term preceding it
Common ratio
a technique for converting a quadratic polynomial of the form ax^{2}+bx+c to the form a^{2}+k} for some values of h and k
completing the square
each of two complex numbers having their real parts identical and their imaginary parts of equal magnitude but opposite sign. a+bi, a-bi
complex conjugates
a fraction in which numerator, denominator, or both are themselves fractions
complex fraction
a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a symbol called the imaginary unit, and satisfying the equation i2 = −1.
Complex number
an operation that takes two functions f and g and produces a function h such that h(x) = g(f(x))
Composition of functions
an inequality that combines two simple inequalities.
Compound inequality
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.
Conic section
if there is at least one set of values for the unknowns that satisfy each equation in the system
Consistent
the constant (unchanged) ratio of two variable quantities. The formula for direct variation is. y=kx (or y=kx )
constant of variation
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
continuous relation
a number between −1 and +1 calculated so as to represent the linear dependence of two variables or sets of data.
correlation coefficient
the one that depends on the value of some other number
dependent
the number of rows by the number of columns. If a matrix has a rows and b columns, it is an a×b matrix.
dimensions of a matrix
describes a simple relationship between two variables . We say y varies directly with x if: y=kx. for some constant k
direct variation
a function of the coefficients of a polynomial equation whose value gives information about the roots of the polynomial. b2-4ac
discriminant
a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant, or resulting when a cone is cut by an oblique plane which does not intersect the base.
ellipse
the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
end behavior
a function of the form f(x)=ab^{x} where b is a positive real number, and the argument x occurs as an exponent
exponential equation
a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem
extraneous solution
the maximum or minimum value of a function.
. extrema
a theorem linking factors and zeros of a polynomial. The theorem states that a polynomial f(x) has a factor if and only if f(k)=0.
factor theorem
A sequence that has a limited number of terms
finite sequence
a relationship or expression involving one or more variables.
. function
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
geometric sequence
a function that returns a constant value for each specific interval
greatest integer function
the factor by which a quantity multiplies itself over time. The rate is the addend by which a quantity increases (or decreases) over time
growth factor
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.
hyperbola
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
identity function
a solution to the quadratic equation x² + 1 = 0
imaginary unit
If a system has no solution,
inconsistent
a variable that represents a quantity that is being manipulated in an experiment
independent
a list or string of discrete objects, usually numbers, that can be paired off one-to-one with the set of positive integers 1, 2, 3,
infinite sequence
a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval that contains 0, 1, and all numbers in between
interval notation
a function that undoes the action of the another function. A function g is the inverse of a function f if whenever y=f(x) then x=g(y).
inverse function
An inverse relationship is the reverse of another or when one variable factor increases, the other decreases.
inverse relation
mathematical relationship between two variables which can be expressed by an equation in which the product of two variables is equal to a constant.
inverse variation
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.
joint variation
a chord of a conic section (such as an ellipse) that passes through a focus and is parallel to the directrix.
latus rectum
a mathematical technique for maximizing or minimizing a linear function of several variables, such as output or cost.
linear programming
a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
logarithm
a common S-shaped curve , the x value of the sigmoid’s midpoint; L, the curve’s maximum value; k, the logistic growth rate or steepness of the curve. x and y axes increase
logistic growth model
a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.
matrix
An nth root of a number x, where n is a positive integer, is any of the n real or complex numbers r whose nth power is x
nth root
a logarithm to the base e (2.71828…).
natural logarithm
how many times to divide by the number.
negative exponent
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.
parabola
the simplest function of a family of functions that preserves the definition (or shape) of the entire family
parent function
one which is defined not by a single equation, but by two or more. Each equation is valid for some interval
piece wise defined function
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
slope form
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
quadratic function
The value inside the radical symbol.
radicand
a rate that describes how one quantity changes in relation to another quantity
rate of change
an exponent that is a fraction.
rational exponent
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.
rational function
to eliminate any radical expressions in the denominator such as square roots and cube roots.
rationalizing the denominator
a formula that defines each term of a sequence using preceding term(s).
recursive formula
a line that best describes the behavior of a set of data
regression line
a point where the function changes direction from increasing to decreasing
relative maximum
all the points x, in the domain of the function, such that it is the smallest value for some neighborhood
relative minimum
a solution to an equation, usually expressed as a number or an algebraic formula.
root
a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.
scatter plot
an enumerated collection of objects in which repetitions are allowed and order matters
sequence
a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy.
set builder notation
a function that increases or decreases abruptly from one constant value to another.
step function
a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor
synthetic division
a point where two or more curves, lines, or edges meet.
vertex form
a method that is used to determine whether a given relation is a function or not.
vertical line test
a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is the solution to the equation f(x) = 0.
zeros
