1.
Arithmetic Sequence: a sequence in which each term after the first is found by adding a constant, the common difference "d", to the previous term
2.
Asymptote: a line that a graph approches
3.
Change of base formula: for all positive numbers, "a", "b", "n", where a ≠ 1, b ≠ 1
Loga N= logbN/logbA
4.
circle: the set of all points in a plane that are equidistant from a given point in the plane, called the center
5.
Combined variation: when one quantity varies directly and/ or inversely as two or more other quantities
6.
common difference: the difference between the successive terms of an arithmetic sequence
7.
common logarithm: logarithms that use 10 as the base
8.
common ratio: the ratio of successive terms of a geometric sequence
9.
completing the square: a process used to make a quadratic expression into a perfect square trinomial
10.
complex conjugates: two complex numbers of the form a+bi and a-bi
11.
complex fraction: a rational expression whose numerator and/ or denominator contains a rational expression
12.
complex number: any number that can be written in the form a+bi, where a and b are real numbers and i is the imaginary unit
13.
composition of functions: a function is performed, and then a second fuction is performed on the result of the first function. The composition of f and g is denoted by f•g, and [f•g](x)= f[g(x)].
14.
compound inequality: two inequalities joined by the word "and" or "or"
15.
conic section: any figure that can be obtained by slicing a double cone
16.
consistent: a system of equation that has at least one solution
17.
constant of variation: the constant k used with direct or inverse variation
18.
continuous relation: a relation that can be graphed with a line or smooth curve
19.
correlation coefficient: a measure that shows how well data are modeled by a linear equation
20.
dependent: when a system of linear equations has an infinite number of solutions
21.
dimensions of a matrix: the number of rows, m, and the number of columns, n, of the matrix written as m x n
22.
direct variation: y varies directly as x if there is some nonzero constant k such that y=kx. k is called the constant of variation
23.
discriminant: in the quadratic formula, the expression b^2 -4ac
24.
ellipse: the set of all points in a plane such that the sum of the distances from two given points in the plane, called foci, is constant
25.
end behavior: the behavior of the graph as x approaches positive infinity or negative infinity
26.
exponential equation: an equation in which the variables occur as exponents
27.
extraneous solution: a number that does not satisfy the original equation
28.
extrema: the max and min values of a function
29.
factor theorem: the binomial x-r is a factor of the polynomial P(x) if and only if P(r)=0
30.
Finite sequence: a sequence containing a limited number of terms
31.
function: a relation in which each element of the domain is paired with exactly one element in the range
32.
geometric sequence: a sequence in which each term after the first is found by multiplying the previous term by a constant r, called the common ratio
33.
greatest integer function: a step function, written as f(x)=[[x]], where f(x) is the greatest integer less than or equal to x
34.
growth factor: in exponential growth, the base of the exponential expression, 1+r
35.
hyperbola: the set of all points in the plane such that the absolute value of the difference of the distances from two given points in the plane, called foci, is constant
36.
identity function: the function I(x)=x
37.
imaginary unit: i, or the principal square root of -1
38.
inconsistent: a system of equations that has no solutions
39.
independent: when a system of linear equations has exactly one solution
40.
infinite sequence: a sequence that continues without end
41.
interval notation: a way to describe the solution set of an inequality
42.
inverse function: two functions f and g are inverse functions iff both of their compositions are the identity function
43.
inverse relation: two relations are inverse relations iff whenever one relation contains the element (a,b) the other relation contains the element (b,a)
44.
inverse variation: y varies inversely as x if there is some nonzero constant k such that xy=k or y=k/x where x≠0 and y≠0
45.
joint variation: y varies jointly as x and z if there is some nonzero contant k such that y=kxz
46.
latus rectum: the line segment through the focus of a parabola and perpendicular to the axis of symmetry
47.
linear programming: the process of finding the max or min values of a function for a region defined by inequalities
48.
logarithm: in the function x=b^y,y is called the log base b, of x. Usually written as y=〖log〗_b x and is read "y equals log base b of x"
49.
logistic growth model: a growth model that represents growth that has a limiting factor. Logistic models are the most accurate models for representing population growth.
50.
matrix: any rectangular array of variables or contants in horizontal rows and vertical columns
51.
natural logarithm: logarithms with base e written lnx
52.
negative exponent: for any real number a≠0 and any integer n, a^-n= 1/a^n and 1/a^-n= a^n
53.
nth root: for any real numbers a and b and any positive integer n, if a^n =bthen a is an nth root of b
54.
parabola: the graph of a quadratic function. The set of all points in a plane that are the same distance from a given point, called the focus, and a given line, called the directrix
55.
parent function: the simplest most general function in a family of function
56.
piece wise defined function: a function that is written using two or more expressions
57.
point slope form: an equation in the form y-y1= m(x-x1) where (x1,y1) are the coordinates of a point on the line and m is the slope of a line
58.
quadratic function: a function described by the equation f(x)= ax^2 +bx+c where a≠0
59.
radicand: in nth roots the value inside in the symbol √(n). Indicates the value that is being taken to the nth root
60.
rate of change: how much a quantity changes on average relative to the change in another quantity over time
61.
rational exponent: for any nonzero real number b, and any integers m and n, with
except when b<0 and n is even
62.
rational function: an equation of the form f(x)=p(x)/q(x) where p(x) and q(x) are polynomial functions and q(x)≠0
63.
rationalizing the denominator: to eliminate radicals from a denominator or fractions from a radicand
64.
recursive formula: each term is formulated from one or more previous terms
65.
regression line: a line of best fit
66.
relative maximum: a point on the graph of a function where no other nearby points have a greater y coordinate
67.
relative minimum: a point on the graph of a function where no other nearby points have a lesser y coordinate
68.
root: the solutions of a quadratic equation
69.
scatter plot: a set of data graphed as ordered pairs in a coordinate plane
70.
sequence: a list of numbers in a particular order
71.
set builder notation: the expression of the solution set of an inequality for example {xlx>0}
72.
step function: a function whose graph is a series of line segments
73.
synthetic division: a method used to divide a polynomial by a binomial
74.
vertex form: a quadratic function in the form y= a(x-h)^2 +k where (h,k) is the vertex of the parabola and x=h is its axis of symmetry
75.
vertical line test: if no vertical line intersects a graph in more than one point then the graph represents a function
76.
zeros: the x intercepts of the graph of a function the points for which f(x) =0
