Unit 4: Functional Relationships Vocabulary
Internet Resources:
http://www.apskids.org/students.asp
http://www.thinkcentral.com/index.htm – Course 3 Math (see textbook) Keywords from Textbook
http://mathforum.org/library/drmath/drmath.middle.html
http://www.regentsprep.org/Regents/math/ALGEBRA/AE1/indexAE1.htm - Algebraic Translations
http://www.regentsprep.org/Regents/math/ALGEBRA/AE2/indexAE2.htm - Linear Equations
http://www.regentsprep.org/Regents/math/ALGEBRA/AE8/indexAE8.htm - Linear Inequalities
http://www.regentsprep.org/Regents/math/ALGEBRA/AE85/indexAE85.htm - Graphing Liner Inequalities
http://www.regentsprep.org/Regents/math/ALGEBRA/AP3/indexAP3.htm - Functions
http://www.regentsprep.org/Regents/math/ALGEBRA/AC5/LFuncGraph.htm - Graphing Functions
http://www.regentsprep.org/Regents/math/algtrig/ATP2/indexATP2.htm - Arithmetic Sequence
http://www.regentsprep.org/Regents/math/ALGEBRA/AP2/indexAP2.htm - Sets & Venn Diagrams
http://www.regentsprep.org/Regents/math/ALGEBRA/AP1/indexAP1.htm - Interval Notations
Term
Function
Set
Subset
Definition
A relationship that maps an input value with one unique output value. A
special dependence between two quantities where the independent
variable (or input) produces the dependent variable (or output).
A collection of numbers, geometric figures, letters, or other objects that
have some characteristic in common.
A collection of items drawn entirely from a single set. A subset can
consist of any number of items from a set ranging from none at all (a null
subset) all the way up to the entire set (every set is a subset of itself).
A set.
Relation
Union of Sets
The set of all elements that belong to at least one of the given two or more
sets.
A subset that does not contain every element of the parent set.
Proper Subset
A member or item in a set.
Element
A subset which has no elements; also called the ‘empty set’.
Null Set
Intersection of Sets
The set of all elements contained in all of the given sets, but no additional
elements.
(This is also known as the absolute complement of a set and/or the
relative complement of a set.) If a universal set, U, is defined; the
Complement of a Set
complement of A in U is the collection of all items in U not in A and may
Venn Diagram
be denoted by AC or A′.
A picture that illustrates the relationship between two or more sets
{ }: “Curly braces” are often used to denote members of a set. For
example, the positive, single-digit, even numbers are {2,4,6,8}.
Term
Explicit Form of a
Sequence
Definition
See Closed Form of a Sequence.
(This is also known as the explicit form of a sequence.)
For an arithmetic sequence, use as the explicit or closed form.
For a geometric sequence, use as the explicit or closed form.
an represents the nth term of the sequence;
Closed Form of a Sequence
a1 represents the first term in the sequence;
d is the common difference for the arithmetic sequence;
r is the common ratio for the geometric sequence; and
n represents the number of a term (for the 7th term, n would be 7).
This form should be simplified whenever possible.
A set of algebraic expressions that produce the next term in a sequence.
Recursive Form
Symbol
Definition
{}
Set notation.
∈
Is an element of – For example, if A is the set of positive, single-digit,
even number, then 2∈ A.
∉
Is not an element of – For example, if A is the set of positive, single-digit,
even number, then 3∉ A.
⊂
Is a subset of – For example, if A is the set of positive, single-digit, even
number, then {2}⊂ A..
NOTE: Many authors and texts use this symbol only for proper subsets,
but some are not so precise.
Is a subset of – The difference between ⊆ and ⊂ is similar to the
⊆
∪
∩
difference between ≤ and <. For example, if A is the set of positive,
single-digit, even number, then {2,4,6,8}⊆ A. NOTE: While {2,4,6,8} is a
subset of A, it is not a proper subset of A.
Union – Contains every element in the sets, but no additional elements.
For example, if B is the set of even natural numbers and C is the set of
odd natural numbers, then B∪C = {N} where N = the set of all natural
numbers.
Intersection – Contains all elements common to the sets, but no additional
elements. For example, A ∩B = {x | x∈ A and x ∈ B}.