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| the x-value of an ordered pair that describes the vertical distance from the x-axis. It is always written as the first element in the ordered pair. |
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| The absolute value of a real number, x, is the distance from x to the origin on the real number line. |
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| A sequence of steps that produce a desired outcome |
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| Numeric or algebraic input into an algorithm, nth function, or other defined function |
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an action performed on two quantities
(Addition, subtraction, multiplication, division or exponentiation) |
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| The sum or difference of two monomials |
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| A set is said to be closed under some operation if the operation on members of the set produces a member of the set. For example, the real numbers are closed under subtraction, where the subset of natural numbers is not. |
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Any number that can be written in the form a + bi where
a and b are real numbers and i is √-1 (the square root
of -1) |
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Combining two functions by taking the output of one and
using it as the input of another |
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| Consistent system (of equations) |
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| A system of equations that has at least one solution |
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| A function f is decreasing on an interval if and only if for every a and b in the interval, f(a) > f(b) whenever a < b. |
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| A function f is continuous at a point (x,y) if it is defined at that point and passes through that point without a break. |
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| the degree of the term with greatest sum of powers. |
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| Dependent system of equations |
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| System of linear equations where one linear equation is a multiple of the other and, therefore, has an infinite number of solutions |
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| A relationship between two variables, x and y, that can be expressed as y=kx where k is the constant of variation |
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| an algebraic expression related to the coefficients of a quadratic equation that can be used to determine the number and type of solutions to the equation |
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| the set of independent values in a function; the set of first elements in ordered pairs in a function |
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a rule that pairs elements from one set, called the domain, to elements from another set, called the range, in such a way that no first element is repeated
The result is a set of ordered pairs, (x, y) where each x value is unique. Representations of functions include graphs, tables, function notation, mapping diagrams and words. |
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| Fundamental Theorem of Algebra |
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Every polynomial equation with degree greater than zero has at least one root in the set of complex numbers.
Corollary: Every polynomial P(x) of degree n (n > 0) can be written as the product of a constant k (k ≠ 0) and n linear factors |
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| Fundamental Theorem of Arithmetic |
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| The Fundamental Theorem of Arithmetic theory states that every natural number greater than 1 can be written as a unique product of prime numbers. |
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| Inconsistent System of Equations |
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| System of linear equations that has no solutions; parallel lines |
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| A function f is increasing on an interval if and only if f(a) > f(b) for every a > b in the interval. |
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| Independent System of Equations |
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| A consistent system of linear equations with only one solution |
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number indicating what root is being taken
Example: 4√981 where 4 is the index. |
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| Indirect (inverse) variation |
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| A relationship between two variables, x and y, that can be expressed as y = k/x, where k is the constant of variation. |
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| point where a curve crosses the x- or y-axis. |
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a relationship that exists when a quantity varies directly with the product of two or more quantities
y = kxy |
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A function in the form y = mx+b where m and b are constants
The graph of a linear function is a line.
A linear equation has degree 1. |
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| an equation that contains more than one variable; an implicit equation; often mathematical formulae |
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A rectangular table of elements which may be numbers or any abstract quantities that can be added and multiplied; used to describe linear equations, keep track of the coefficients of linear transformations, and to record data that depend on multiple parameters; a key component of linear algebra; dimensions of a matrix--number of rows and the number of columns of a matrix, written r x c
1 5 7 5
4 3 2 0
9 8 0 7 |
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| A value in a data set that is much higher or lower than the rest; a point which falls more than 1.5 times the interquartile range above the third quartile or below the first quartile |
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| A function that can be written as R(x) = P(x) / Q(x) where P(x) and Q(x) are polynomials and Q(x) ≠ 0. |
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| A number x such that P(x)=0. A polynomial of degree n has n roots. |
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| A polynomial expression with three terms |
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| A value of x for which f(x) = 0 |
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