Final Flashcards
a sequence of numbers such that the difference between the consecutive terms is constant (list of numbers with a definite pattern)
Arithmetic sequence
a line that continually approaches a given curve but does not meet it at any finite distance
Asymtote
logba=logda/logdb (rewrite the log base 2 as a logarithm of any other base)
Change of base formula
is a shape consisting of all points in a plane that are at a given distance from a given point
Circle
a variable depends on two (or more) other variables, and varies directly with some of them and varies inversely with others
Combined variation
constant difference between consecutive terms of an arithmetic sequence
Common difference
the logarithm with base 10
common logarithm
the constant factor between consecutive terms of a geometric sequence
common ratio
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
the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.
complex conjugates
a fraction in which the denominator and numerator or both contain 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
complex number
an operation that takes two functions f and g and produces a function h such that h(x) = g. ( applying one function to the results of another)
composition of fractions
a sentence with two inequality statements joined either by the word “or” or by the word “and.”
compound inequality
a curve obtained as the intersection of the surface of a cone with a plane
conic section
system of equations in which at least one set of values for the unknowns that satisfies each equation in the system
consistent
the constant (unchanged) ratio of two variable quantities
constant of variation
a complete range of measurements from one extreme to the other
continuous variation
values belonging to the set can take on ANY value within a finite or infinite interval (no interruptions)
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
reliant on another characteristic
dependent
the number of rows by the number of columns
dimensions of a matrix
describes a simple relationship between two variables
direct variation
quantity that depends on the coefficients and determines various properties of the roots
discriminant
a plane curve surrounding two focal points
ellipse
describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).
end behavior
equations in which variables occur as exponents.
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
any point at which the value of a function is largest (a maximum) or smallest (a minimum)
extrema
used when factoring polynomials “completely” (theorem linking factors and zeros of a polynomial)
factor theorem
a list of terms in a specific order
finite sequence
relation between two sets that associates to each element of the first set exactly one element of the second set
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
function that returns a constant value for each specific interval
greatest integer function
the factor by which a quantity multiplies itself over time
growth factor
a type of smooth curve lying in a plane, defined by its geometric properties
hyperbola
a function that always returns the same value
identity function
a solution to the quadratic equation x² + 1 = 0. (i)
imaginary unit
two or more equations that are impossible to solve based on using one set of values for the variables (system has no solution)
inconsistent
a quantity that is being manipulated in an experiment
independent
a sequence that keep on going and going
infinite sequence
a way to describe continuous sets of real numbers by the numbers that bound them
interval notation
a function that “reverses” another function
inverse function
the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function
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
occurs when a variable varies directly or inversely with multiple variables.
joint variation
a compound of the Latin latus, meaning “side,” and rectum, meaning “straight.”
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 (inverse function to exponentiation)
logarithm
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
logistic growth model
a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns
matrix
any of the n real or complex numbers r whose nth power is x
nth root
a number is its logarithm to the base of the mathematical constant e (LN)
natural logarithm
the base is on the wrong side of the fraction line, so you need to flip the base to the other side
negative exponent
a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side
parabola
the simplest function of a family of functions that preserves the definition of the entire family
parent function
a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain
peicewise defined function
the general form y-y₁=m(x-x₁) for linear equations
point slope form
a function of degree two. The graph of the function is a parabola
quadratic function
the value inside the radical symbol
radicand
the speed at which a variable changes over a specific period of time
rate of change
an exponent that is a fraction
rational exponent
any function which can be written as the ratio of two polynomial functions, where the polynomial in the denominator is not equal to zero
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 terms
recursive formula
represents the relationship between your independent variable and your dependent variable
regression line
a point that is higher than the points directly beside it on both sides
relative maximum
a point that is lower than the points directly beside it on both sides
relative minimum
where a function equals zero
root
a graph in which the values of two variables are plotted along two axes, the pattern of the resulting points revealing any correlation present
scatter plot
a particular order in which related events, movements, or things follow each other
sequence
describes or defines the elements of a set instead of listing the elements
set builder notation
a mathematical function of a single real variable that remains constant within each of a series of adjacent intervals but changes in value from one interval to the next
step function
a simplified method for dividing a polynomial by another polynomial
synthetic division
given by y = a(x – h)2 + k, where (h, k) is the vertex
vertex form
method that is used to determine whether a given relation is a function or not
vertical line test
the points where the graph of the quadratic equation crosses the x-axis
zeros
