Vocab Flashcards
arithmetic sequence
a sequence made by adding the same value each time
asymptote
a line that continually approaches a given curve but does not meet it at any finite distance
change of base formula
a formula that allows you to rewrite a logarithm in terms of logs written with another base
circle
a shape consisting of all points in a plane that are at a given distance from a given point
combined variation
the combination of direct and inverse proportionality
common difference
the constant difference between consecutive terms of an arithmetic sequence
common logarithm
the logarithm with base 10
common ratio
the constant factor between consecutive terms of a geometric sequence
completing the square
a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial
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 complex number is 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
composition of functions
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 where at least one set of values for the unknowns satisfies each equation in the system; when substituted into each of the equations, they make each equation hold true as an identity
constant of variation
the constant (unchanged) ratio of two variable quantities
continuous relation
a set of data is said to be discrete (characterized by integers) if the values belonging to the set are distinct and separate (unconnected values)
correlation coefficient
a number that is a measure of the strength and direction of the correlation between two variables
dependent
the variable 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 (like negative height)
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
a function that always returns the same value that was used as its argument
imaginary unit
a number that when squared gives a negative result
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 (-3≤x≤2)
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 (n as exponent)
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
piece-wise defined function
a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain
point-slope form
derived from the concept of finding the slope of a line when two points are given
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 (line of best fit)
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 {x : x > 0}
step function
a function on the real numbers that can be written as a finite linear combination of indicator functions of intervals (not a continuous line)
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
