Final Vocab Flashcards
arithmetic sequence
sequence where the difference between each term is constant
asymptote
a line that continually approaches a given curve but does not meet it
change of base formula
log base b of a = log base d of a / log base d of b
circle
2D shape where all outer points are the same distance from the center
combined variation
when a variable depends on two or more other variables, and varies directly with some of them and varies inversely with others
common difference
constant difference between consecutive terms of an arithmetic sequence
common logarithm
logarithm with base 10
common ratio
constant factor between consecutive terms of a geometric sequence
completing the square
converting a quadratic trinomial to a binomial squared
complex conjugates
a pair of complex numbers a+bi and a-bi
complex fraction
a fraction that contains a fraction
complex number
any number that can be written in the form a+bi
composition of functions
operation between two functions
compound inequality
two inequalities joined by AND or OR
conic section
curve produced at the intersection of a cone and a plane; hyperbola, parabola, ellipse
consistent
a system of equations with at least one solution
constant of variation
number that relates two or more variables that are directly proportional, inversely proportional, or jointly proportional
continuous relation
data points connected by a line
correlation coefficient
a number between -1 and +1 that represents the linear dependence of two variables
dependent
the variable that changes based on the independent variable being changed
dimensions of a matrix
number of rows and columns in a matrix
direct variation
a simple relationship between two variables; when one variable increases, the other one does too
discriminant
part of the quadratic formula under the square root (b^2-4ac); positive: two real, zero: one solution, negative: two imaginary/complex roots
ellipse
regular oval shape where the sum of the distances between any point on the edge and the two foci is the same all the way around
end behavior
behavior of a graph as x approaches positive infinity or negative infinity
exponential equation
equations where variables occur as exponents
extraneous solution
root of an equation that does not fit into the original equation
extrema
maximum or minimum value of a function
factor theorem
zero product property
finite sequence
list of terms in order with a first term and a last term following a certain pattern
function
relation between two variables
geometric sequence
sequence of numbers where each term is multiplied by a common ratio to get the next term
greatest integer function
function that returns a constant value for each specific interval
growth factor
factor by which a quantity multiplies itself over time
hyperbola
set of all points such that the difference of the distances between a point and the foci is constant
identity function
function that always outputs the same value input
imaginary unit
square root of -1
inconsistent
a system of equations with no solutions
independent
a consistent system of equations with exactly one solution
interval notation
a way to describe continuous sets of real numbers using parentheses/brackets and the numbers on each extreme
inverse function
represented as f of -1 and found by switching the x and y in a function and solving for y
inverse relation
a set of ordered pairs where the x and y values from the original set are swapped
inverse variation
a relation between two variables where one variable increase as the other decreases, and vice versa
joint variation
a relation where one variable depends on two or more other variables, and varies directly as each of them when the others are held constant
latus rectum
chord that passes through the focus of a conic section and is parallel to the directrix
linear programming
a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships
logarithm
a quantity representing the power to which the base must be raised to produce a given number
logistic growth model
s shaped curve
matrix
a rectangular array of values for which operations such as addition and multiplication are defined
nth root
the nth root of x is r
natural logarithm
logarithm to the base e
negative exponent
flips the base
parabola
symmetrical curve formed by the intersection of a cone with a plane parallel to its side
parent function
simplest function of a family of functions that preserves the definition of the entire family
piece-wise defined function
a function that is defined by two or more equations
point-slope form
y-y1=m(x-x1)
quadratic function
a polynomial function in which the highest-degree term is of the second degree
radicand
the value inside the radical symbol
rate of change
a rate that describes how one quantity changes in relation to another quantity
rational exponent
an exponent that is a function
rational function
any function which can be defined by a rational fraction
rationalizing the denominator
eliminating any radical expressions in the denominator
recursive formula
a formula that defines each term of a sequence using preceding terms and must always state the initial term
regression line
line of best fit
relative maximum
the highest point in a particular section of a graph
relative minimum
the lowest point in a particular section of a graph
root
values of a variable for which a polynomial equals zero
scatter plot
a graph in which the values of two variables are plotted along two axes, showing any correlation present between them
sequence
a list of numbers in a specific order
set-builder notation
describes a set by stating the properties it must satisfy
step function
a piece-wise constant function having only finitely many pieces
synthetic division
dividing polynomials using less writing and calculation than long division
vertex form
y=a(x-h)^2+k, where (h,k) is the vertex
vertical line test
method to determine whether a relation is a function or not
zeros
a value of x that, when plugged into a function, outputs zero
