 Hazleton Area High School
 PRECALCULUS VOCABULARY

SECTION
WORD
DEFINITION
1
1.1
Cartesian Coordinate System
A coordinate system in which the coordinates of a point are its distances from a set of perpendicular lines that intersect at an origin, such as two lines in a plane; or called the rectangular coordinate system
2
1.2
Relation
Any set of ordered pairs
3
1.2
Domain
The set of all first components of the ordered pairs
4
1.2
Range
The set of all second components of the ordered pairs
5
1.2
Function
A relation in which no two ordered pairs have the same first component and different second components
6
1.2
Vertical line test for function
If any vertical line intersects a graph in more than one point, the graph does not define y as a function of x
7
1.3
Relative Maximum
The points at which a function changes from increasing to decreasing
8
1.3
Relative Minimum
The points at which a function changes from decreasing to increasing
9
1.8
Horizontal Line Test for Inverse Functions
A function f has an inverse that is a function f^{1}, if there is no horizontal line that intersects the graph of the function f at more than one point
10
1.10
Quadratic Function
Any function in the form of f(x) = ax^{2} +bx +c where a≠ 0
11
2.2
Parabola
The graph of any quadratic function
12
2.3
Polynomial Functions
Have a degree 2 or higher have graphs that are smooth and continuous curves
13
2.6
Rational Functions
Quotients of polynomial functions expressed as
14
3.1
Exponential Functions
Functions whose equations contain a variable in the exponent
15
3.4
Exponential Equation
An equation containing a variable in an exponent
16
7.1
Inconsistent System
A linear system of equations with no solutions
17
7.1
Consistent System
A linear system of equations with at least one solution
18
7.1
Dependent
A linear system of equations with infinitely many solutions
19
8.1
Matrix (plural: Matrices)
Arranging numbers in rows and column and placed in brackets
20
8.1
Elements
The numbers inside the brackets of the matrix
21
8.1
Augmented matrix
A vertical bar separating the columns of the matrix into two groups; The coefficients of each variable are placed to the left of the vertical line and the constants are placed to the right
22
8.1
Gaussian Elimination
The process used to solve linear systems using matrix row operations after the German mathematician
23
8.3
Equality of Matrices
Two matrices A and B are equal if and only if they have the same order m x n and a_{ij} = b_{ij} for i = 1, 2, ….m and j = 1, 2, …n
24
8.3
Matrix Multiplication
The product of an m x n matrix, A, and n x p matrix, B, is an m x p, AB, whose elements are found as follows. The element in the ith row and jth column of AB is found by multiplying each element in the ith row of A by the corresponding element in the jth column of B and adding the products
25
8.4
Multiplicative identity matrix of order n
The n x n square matrix with Is down the main diagonal from upper left to lower right and 0s elsewhere
26
8.5
Determinant
Associated with every square matrix is a real number
27
8.5
Cramer’s Rule
The method of using determinants to solve the linear system
28
10.1
Infinite Sequence
A function whose domain is the set of positive integers. The function values or terms of the sequence are represented by a_{1}, a_{2} , a_{3}, a_{4},…. a_{n}
29
10.1
Finite Sequence
Sequences whose domains consist only of the first n positive integers
30
10.1
Factorial Notation
Products of consecutive positive integers expressed in special notation n! The product of all positive integers from n down through 1
31
10.2
Arithmetic Sequence
A sequence in which each term after the first differs from the preceding term by a constant amount
32
10.2
Common Difference
The difference between consecutive terms of the sequence
33
10.3
Geometric Sequence
A sequence in which each term after the first is obtained by multiplying the preceding term by a fixed nonzero constant.
34
10.3
Common Ratio
The amount by which we multiply each time of the sequence
35
10.3
Annuity
A sequence of equal payments made at equal time periods. An IRA is an example of an annuity
SECTION
WORD
DEFINITION
1
1.1
Cartesian Coordinate System
A coordinate system in which the coordinates of a point are its
distances from a set of perpendicular lines that intersect at an origin, such
as two lines in a plane; or called the rectangular coordinate system
2
1.2
Relation
Any set of ordered pairs
3
1.2
Domain
The set of all first components of the ordered pairs
4
1.2
Range
The set of all second components of the ordered pairs
5
1.2
Function
A relation in which no two ordered pairs have the same first
component and different second components
6
1.2
Vertical line test for
function
If any vertical line intersects a graph in more than one point, the
graph does not define y as a function of x
7
1.3
Relative Maximum
The points at which a function changes from increasing to decreasing
8
1.3
Relative Minimum
The points at which a function changes from decreasing to increasing
9
1.8
Horizontal Line Test for
Inverse Functions
A functionfhas an inverse
that is a functionf^{1},
if there is no horizontal line that intersects the graph of the functionfat more than one point
10
1.10
Quadratic Function
Any function in the form of
f(x) = ax^{2}+bx +c where
a≠0
11
2.2
Parabola
The graph of any quadratic function
12
2.3
Polynomial Functions
Have a degree 2 or higher have graphs that are smooth and continuous
curves
13
2.6
Rational Functions
Quotients of polynomial functions expressed as
, wherep
andqare polynomial functions andq(x)≠0
14
3.1
Exponential Functions
Functions whose equations contain a variable in the exponent
15
3.4
Exponential Equation
An equation containing a variable in an exponent
16
7.1
Inconsistent System
A linear system of equations with no solutions
17
7.1
Consistent System
A linear system of equations with at least one solution
18
7.1
Dependent
A linear system of equations with infinitely many solutions
19
8.1
Matrix (plural: Matrices)
Arranging numbers in rows and column and placed in brackets
20
8.1
Elements
The numbers inside the brackets of the matrix
21
8.1
Augmented matrix
A vertical bar separating the columns of the matrix into two groups;
The coefficients of each variable are placed to the left of the vertical line
and the constants are placed to the right
22
8.1
Gaussian Elimination
The process used to solve linear systems using matrix row operations
after the German mathematician
23
8.3
Equality of Matrices
Two matrices A and B are equal if and only if they have the same
order m x n and a_{ij}= b_{ij}fori= 1, 2, ….mandj= 1, 2, …n
24
8.3
Matrix Multiplication
The product of anmxnmatrix, A, andnxpmatrix, B, is anmxp,AB, whose elements are found as follows. The element in theith row andjth column
of AB is found by multiplying each element in theith row ofAby the
corresponding element in thejth
column ofBand adding the products
25
8.4
Multiplicative identity matrix
of order n
Thenxnsquare matrix with Is down the main diagonal from upper left
to lower right and 0s elsewhere
26
8.5
Determinant
Associated with every square matrix is a real number
27
8.5
Cramer’s Rule
The method of using determinants to solve the linear system
28
10.1
Infinite Sequence
A function whose domain is the set of positive integers. The function values or terms of the
sequence are represented bya_{1},
a_{2}, a_{3}, a_{4},…. a_{n}
29
10.1
Finite Sequence
Sequences whose domains consist only of the firstnpositive integers
30
10.1
Factorial Notation
Products of consecutive positive integers expressed in special
notationn! The product of all positive integers fromndown through 1
31
10.2
Arithmetic Sequence
A sequence in which each term after the first differs from the
preceding term by a constant amount
32
10.2
Common Difference
The difference between
consecutive terms of the sequence
33
10.3
Geometric Sequence
A sequence in which each term after the first is obtained by
multiplying the preceding term by a fixed nonzero constant.
34
10.3
Common Ratio
The amount by which we multiply each time of the sequence
35
10.3
Annuity
A sequence of equal payments made at equal time periods. An IRA is an example of an annuity
SECTION
WORD
DEFINITION
1
1.1
Cartesian Coordinate System
A coordinate system in which the coordinates of a point are its
distances from a set of perpendicular lines that intersect at an origin, such
as two lines in a plane; or called the rectangular coordinate system
2
1.2
Relation
Any set of ordered pairs
3
1.2
Domain
The set of all first components of the ordered pairs
4
1.2
Range
The set of all second components of the ordered pairs
5
1.2
Function
A relation in which no two ordered pairs have the same first
component and different second components
6
1.2
Vertical line test for
function
If any vertical line intersects a graph in more than one point, the
graph does not define y as a function of x
7
1.3
Relative Maximum
The points at which a function changes from increasing to decreasing
8
1.3
Relative Minimum
The points at which a function changes from decreasing to increasing
9
1.8
Horizontal Line Test for
Inverse Functions
A functionfhas an inverse
that is a functionf^{1},
if there is no horizontal line that intersects the graph of the functionfat more than one point
10
1.10
Quadratic Function
Any function in the form of
f(x) = ax^{2}+bx +c where
a≠0
11
2.2
Parabola
The graph of any quadratic function
12
2.3
Polynomial Functions
Have a degree 2 or higher have graphs that are smooth and continuous
curves
13
2.6
Rational Functions
Quotients of polynomial functions expressed as
, wherep
andqare polynomial functions andq(x)≠0
14
3.1
Exponential Functions
Functions whose equations contain a variable in the exponent
15
3.4
Exponential Equation
An equation containing a variable in an exponent
16
7.1
Inconsistent System
A linear system of equations with no solutions
17
7.1
Consistent System
A linear system of equations with at least one solution
18
7.1
Dependent
A linear system of equations with infinitely many solutions
19
8.1
Matrix (plural: Matrices)
Arranging numbers in rows and column and placed in brackets
20
8.1
Elements
The numbers inside the brackets of the matrix
21
8.1
Augmented matrix
A vertical bar separating the columns of the matrix into two groups;
The coefficients of each variable are placed to the left of the vertical line
and the constants are placed to the right
22
8.1
Gaussian Elimination
The process used to solve linear systems using matrix row operations
after the German mathematician
23
8.3
Equality of Matrices
Two matrices A and B are equal if and only if they have the same
order m x n and a_{ij}= b_{ij}fori= 1, 2, ….mandj= 1, 2, …n
24
8.3
Matrix Multiplication
The product of anmxnmatrix, A, andnxpmatrix, B, is anmxp,AB, whose elements are found as follows. The element in theith row andjth column
of AB is found by multiplying each element in theith row ofAby the
corresponding element in thejth
column ofBand adding the products
25
8.4
Multiplicative identity matrix
of order n
Thenxnsquare matrix with Is down the main diagonal from upper left
to lower right and 0s elsewhere
26
8.5
Determinant
Associated with every square matrix is a real number
27
8.5
Cramer’s Rule
The method of using determinants to solve the linear system
28
10.1
Infinite Sequence
A function whose domain is the set of positive integers. The function values or terms of the
sequence are represented bya_{1},
a_{2}, a_{3}, a_{4},…. a_{n}
29
10.1
Finite Sequence
Sequences whose domains consist only of the firstnpositive integers
30
10.1
Factorial Notation
Products of consecutive positive integers expressed in special
notationn! The product of all positive integers fromndown through 1
31
10.2
Arithmetic Sequence
A sequence in which each term after the first differs from the
preceding term by a constant amount
32
10.2
Common Difference
The difference between
consecutive terms of the sequence
33
10.3
Geometric Sequence
A sequence in which each term after the first is obtained by
multiplying the preceding term by a fixed nonzero constant.
34
10.3
Common Ratio
The amount by which we multiply each time of the sequence
35
10.3
Annuity
A sequence of equal payments made at equal time periods. An IRA is an example of an annuity