Final Flashcards
Arithmetic Sequence
a sequence in which the difference of consecutive terms in constant
asymptote
a line that a graph approaches more and more closely
change of base formula
A formula that allows you to rewrite a logarithm in terms of logs written with another base.
circle
a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).
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 (when the rest of the variables are held constant).
common difference
The constant difference between consecutive terms of an arithmetic sequence
common logarithm
a logarithm to the base 10.
common ratio
The constant factor between consecutive terms of a geometric sequence
completing the square
to add a term c to an expression of the form x²+bx such that x²+bx+c is a perfect square trinomial
complex conjugates
pairs of complex numbers of the forms a+bi and a-bi, where b/=0
complex fractions
a fraction that contains a fraction in its numerator or denominator
complex number
a number written in the form a+bi, where a and b are real numbers
composition of functions
an operation that can be performed with two functions
compound inequality
a sentence with two inequality statements joined either by the word “or” or by the word “and.”
conic section
a figure formed by the intersection of a plane and a right circular cone.
consistent
a linear or nonlinear system of equations
constant of variation
the constant a in the inverse variation equation y-a/x, where a/=0
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 r from -1 to 1 that measures how well a line fits a set of data pairs (x,y)
dependent
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.
dimensions of a matrix
The dimensions of a matrix with m rows and n columns are m x n
direct variation
a simple relationship between two variables
discriminant
The expression b²-4ac in the Quadratic Formula
elipse
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.
end behavior
The behavior of the graph of a function as x approaches positive infinity or negative infinity
exponential equation
equations in which variable expressions occur as exponents
extraneous solution
solutions that are not solutions of the original equation
extrema
the maximum or minimum value of a function.
factor theorem
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.
finite sequence
a list of terms in a specific order.
function
a relationship or expression involving one or more variables.
geometric sequence
a sequence in which the ratio of any term to the previous term is constant
greatest integer function
a function that returns a constant value for each specific interval.
growth factor
the value of b in an exponential growth function of the form y=ab*, where a>0 and b>1
hyperbola
an open curve with two branches, the intersection of a plane with both halves of a double cone.
identity function
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=(square root of)-1
inconsistent
not staying the same throughout.
independent
a variable (often denoted by x ) whose variation does not depend on that of another.
infinite sequence
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, …}.
interval notation
a way to describe continuous sets of real numbers by the numbers that bound them.
inverse function
functions that undo each other
inverse relation
the relation that occurs when the order of the elements is switched in the relation
inverse variation
two variables x and y show inverse variation y=a/x, where a/=0
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 line segment through the focus of a parabola
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.
logarithm
the inverse function to exponentiation.
logistic growth model
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 arrangement of numbers
nth root
for an integer n greater than 1, if b*=a, then b is an nth root of a
natural logarithm
s its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x.
negative exponent
that the base is on the wrong side of the fraction line, so you need to flip the base to the other side.
parabola
the graph of a quadratic function
parent function
the most basic function in a family of functions
piece-wise defined function
a function defined by two or more equations
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.
quadratic function
a function that can be written in the form f(x)=a(x-h)²+k, where a/=0
radicand
The value inside the radical symbol. The value you want to take the root of.
rate of change
mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable.
rational exponent
an exponent that is a fraction.
rational function
a function that has the form f(x)=p
9(x)/q(x), where p(x) and q(x) are polynomials and q(x)/=0
rationalizing the denominator
to eliminate any radical expressions in the denominator such as square roots and cube roots.
recursive formula
a formula that defines each term of a sequence using preceding term(s).
regression line
a straight line that describes how a response variable y changes as an explanatory variable x changes.
relative maximum
a point where the function changes direction from increasing to decreasing (making that point a “peak” in the graph). high
relative minimum
a point where the function changes direction from decreasing to increasing (making that point a “bottom” in the graph). low
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 piecewise 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/=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.
zeros
an x-value of a function f for which f(x)=0
