Finals Vocab 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
Change of base formula
logba=logda/logdb
Circle
a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).
combined variation
y=(kx)/z
common difference
the constant distance d between consecutive terms of n arithmetic sequence
common logarithm
a logarithm with a base 10, between consecutive terms of an arithmetic sequence.
common ratio
the constant r between consecutive terms of a geometric sequence
completing the square
To add a term c to an expression of the form x²+bx+c is a perfect square
complex conjugates
pairs of complex numbers of the forms a+bi and a-bi, where b does not equal 0
complex fraction
a fraction that contains a fraction 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 a function
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.” “And” indicates that both statements of the compound sentence are true at the same time. It is the overlap or intersection of the solution sets for the individual statements.
conic section
a curve obtained as the intersection of the surface of a cone with a plane
consistent
an equation that has at least one set of values for the unknowns that satisfies each equation in the system
constant of variation
the constant a in the inverse variation equation y=a/x, where a does not equal 0
continuous relation
A set of data is where 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
dependant
The dependent variable is the one that depends on the value of some other number
dimensions of a matrix
the number of rows by the number of columns
direct variation
a simple relationship between two variables
discriminant
a quantity that depends on the coefficients and determines various properties of the roots
ellipse
a plane curve surrounding two focal points
end behavior
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}, where b is a positive real number, and the argument x occurs as an exponent
extraneous solution
a solution that emerges from the process of solving the problem but is not a valid solution to the problem
extrema
collectively known as the maxima and minima of a function
factor theorem
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
a function that returns a constant value for each specific interval
growth factor
the factor by which a quantity multiplies itself over time
hyperbola
a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set
identity function
identity function
imaginary unit
a solution to the quadratic equation x² + 1 = 0
inconsistent
the study of commonplace mathematical objects, like sets, numbers, and functions, where some contradictions are allowed
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
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
a variable varies directly or inversely with multiple variables. For instance, if x varies directly with both y and z, we have x = kyz
latus rectum
the chord through a focus parallel to the conic section directrix
linear programming
a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships
logarithm
the inverse function to exponentiation
logistic growth model
a common S-shaped curve
matrix
a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns
n* root
a number r which, when raised to the power n, yields x
natural logarithm
logarithm to the base of the mathematical constant e
negative exponent
how many times to divide by the number
parabola
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
the simplest function of a family of functions that preserves the definition of the entire family
a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain
point-slope form
point-slope form
quadratic function
a polynomial function with one or more variables in which the highest-degree term is of the second degree
radicand
the thing we are finding the root of
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, which is an algebraic fraction such that both the numerator and the denominator are polynomials
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
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, such that it is the smallest value for some neighborhood
root
a value that, when multiplied by itself, gives the number
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
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 that can be written as a finite linear combination of indicator functions of intervals
synthetic division
a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division
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
a member x of the domain of f such that f(x) vanishes at x
