Sem 2 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
change of base formula
logb a=logd a/logd b
circle
shape consisting of all points in a plane that are at a given distance from a given point
combined variation
a situation where a variable depends on two (or more) other variables, and varies directly with some of them and varies inversely with others
common difference
the constant difference d between consecutive terms of an arithmetic sequence
common logarithm
a logarithm with base 10
common ratio
the constant ratio r between consecutive terms of a geometric sequence
completing the square
to add a term c to an expression of the form x^2+bx+c is a perfect square trinomial
complex conjugates
pairs of complex numbers of the forms a+bi and a-bi, where b≠0
complex fraction
a fraction that contains 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 functions
an operation that can be performed with two functions
compound inequalities
an inequality that combines two simple inequalities
conic section
a figure formed by the intersection of a plane and a right circular cone
consistent
a linear or nonlinear system of equations
constant of variation
the constant a in the inverse variation y=a/x, where a≠0
continuous relation
continuous in the usual sense and a composition of continuous relations is continuous
correlation coefficient
a number r from -1 to 1 that measures how well a line fits a set of data pairs (x,y)
dependant
the variable that depends on the value of some other number
dimensions of a matrix
the dimensions of a matrix with m rows and n columns are m x n
direct variation
simple relationship between two variables
discriminant
the expression b^2 -4ac in the quadratic formula
ellipse
a plane curve surrounding two focal points
end behavior
the behavior of the graph of a function as x approaches positive infinity or negative infinity
exponential equation
equation in which variable expressions occur as exponents
extraneous solution
solutions that are not solutions of the original equation
extrema
the maximum or minimum value of a function
factor theorem
a theorem linking factors and zeros of a polynomial
finite sequence
a sequence that comes to an end
function
a relationship or expression involving one or more variables
geometric sequence
a sequence in which the ratio of any term to the previous term is constant
greatest integer function
a function that returns a constant value for each specific interval
growth factor
the value b in an exponential growth function of the form y=ab^x, where a>0 and b>1
hyperbola
a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone
identity function
a function that always returns the same value that was used as its argument
imaginary unit
the square root of -1
inconsistent
a system with no solution
independent
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 integer
interval notation
a number that can be written without a fractional component
inverse functions
functions that undo themselves
inverse relation
set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function
inverse variation
two variables x and y show inverse variation whe y=a/x, when a≠0
joint variation
a variable that varies directly or inversely with multiple variables
latus rectum
is the chord (line segment) that passes through the focus
linear programming
a mathematical technique for maximizing or minimizing a linear function of several variables, such as output or cost
logarithm
a quantity representing the power to which a fixed number (the base) must be raised to produce a given number
matrix
rectangular arrangement of numbers
nth root
for an integer n greater than 1, if b^n=a, then b is an nth root of a
natural logarithm
a logarithm with base e
negative exponent
how many times to divide by the number
parabola
graph of a quadratic function
parent function
the most basic function in a family of functions
piece-wise defined function
function defined by two or more equations
point slope form
y-y1=m(x-x1)
quadratic function
function that can be written in the form f(x)=a(x-h)+k
radicand
the value inside the radical symbol
rate of change
the speed at which a variable changes over a specific period of time
rational exponent
an exponent that is a fraction
rational function
function that has the form f(x)=p(x)/q(x)
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
relative minumum
all the points x, in the domain of the function, such that it is the smallest value for some neighborhood
relative maximum
a point where the function changes direction from increasing to decreasing
root
solution of an equation
scatter plot
a graph in which the values of two variables are plotted along two axes, the pattern of the resulting points revealing any correlation present
sequence
an ordered list of numbers
set-builder notation
uses symbols to define a set in terms of properties of the members of the set
step function
a piecewise function defined by a constant value over each part of its domain
synthetic division
shortcut method to divide a polynomial by a binomal of the form x-h
vertex form
a quadratic function wrtten in the form f(x)=a(x-h)^x+k
vertical line test
a method that is used to determine whether a given relation is a function or not
zeros
an x-value of a function f for which f(x)=0
