Final Flashcards
arithmetic sequence
a sequence in which the difference of consecutive terms is constant
asymptote
a line that a graph approaches more and more closely
common difference
the common difference d between consecutive terms of an arithmetic sequence
common logarithm
the logarithm with base 10
common ratio
constant factor between consecutive terms of a geometric sequence
completing the square
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
complex conjugates
the number with an equal real part and an imaginary part equal in magnitude but opposite in sign
complex fraction
a fraction in which numerator, denominator, or both are themselves fractions
complex number
a number that can be expressed in the form a + bi
composition of function
an operation that takes two functions f and g and produces a function h
compound inequality
an inequality that combines two simple inequalities
conic section
a curve obtained as the intersection of the surface of a cone with a plane
consistent
a linear or nonlinear system of equations
constant of variation
the constant ratio of two variable quantities
continuous relation
if the values belonging to the set can take on ANY value within a finite or infinite interval
correlation coefficiant
a number that is a measure of the strength and direction of the correlation between two variables
dependent
the one that depends on the value of some other number
dimensions of a matrix
the number of rows by the number of columns, if a matrix has a rows and b columns, it is an a×b matrix
direct variation
mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant
discriminant
a quantity that depends on the coefficients and determines various properties of the roots
elipse
a plane curve surrounding two focal points, such that for all points on the curve
end behavior
a function f describes the behavior of the graph of the function at the “ends” of the x-axis
exponential equation
a function of the form f(x)=ab^{x}
extraneous solution
a root of a transformed equation that is not a root of the original equation because it was excluded from the domain of the original
extrema
any point at which the value of a function is largest
factor theorem
the factor theorem is a theorem linking factors and zeros of a polynomial
finite sequence
a list of terms in a specific order
function
a binary relation between two sets that associates to each element of the first set exactly one element of the second set
geometric sequence
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
greatest integer function
the function rounds -off the real number down to the integer less than the number
growth factor
the factor by which a quantity multiplies itself over time
hyperbola
a hyperbola is a type of smooth curve lying in a plane
identity function
a function that always returns the same value that was used as its argument
imaginary unit
a solution to the quadratic equation x² + 1 = 0
inconsistent
when you graph the equations, both equations represent the same line, if a system has no solution
independent
a variable that represents a quantity that is being manipulated in an experiment
infinite sequence
a list or string of discrete objects, usually numbers, that can be paired off one-to-one with the set of positive integers
interval notation
a set of real numbers that contains all real numbers lying between any two numbers of the set
inverse function
a function that “reverses” another function
inverse relation
the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function
change of base formula
a formula that allows you to rewrite a logarithm in terms of logs written with another base
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
joint variation
occurs when a variable varies directly or inversely with multiple variables
latus rectum
the chord through a focus parallel to the conic section directrix
linear programming
modeling technique in which a linear function is maximized or minimized when subjected to various constraints
logarithm
the logarithm is 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 array or table of numbers, symbols, or expressions,
nth root
a number x is a number r which, when raised to the power n, yields r^{n}=x, where n is a positive integer,
natural logarithm
its logarithm to the base of the mathematical constant e
negative exponent
means how many times to divide by the number.
parabola
a parabola is a plane curve which is mirror-symmetrical and is approximately u-shaped
parent function
the simplest function of a family of functions that preserves the definition of the entire family
piece - wise defined function
defined by multiple sub-functions, where each sub-function applies to a different interval in the domain
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
quadratic function
a polynomial function with one or more variables in which the highest-degree term is of the second degree
radicand
the value inside the radical symbol, the value you want to take the root of. In √x, “x”
rate of change
used to 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
any function which can be defined by a rational fraction
rationalizing the denominator
means 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 terms
regression line
an estimate of the line that describes the true, but unknown, linear relationship between the two variables
relative maximum
a point where the function changes direction from increasing to decreasing
relative minimum
all the points x, in the domain of the function
root
a number x is another number, which when multiplied by itself a given number of times, equals x
scatter plot
a type of plot or mathematical diagram using cartesian coordinates to display values for typically two variables for a set of data
sequence
is an enumerated collection of objects in which repetitions are allowed and order matters
set - builder notation
a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy
step function
a function on the real numbers
synthetic division
a method for manually performing euclidean division of polynomials
vertex form
a point where two or more curves, lines, or edges meet
vertical line test
a visual way to determine if a curve is a graph of a function or not
zeros
of a real-, complex-, or generally vector-valued function
circle
a shape consisting of all points in a plane that are at a given distance from a given point
combined variation
describes a situation where a variable depends on two (or more) other variables, and varies directly with some of them and varies inversely with others
