# Math Vocabulary Final

## 76 terms

### 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

### Asymptote

a line that a graph approches

### Change of base formula

for all positive numbers, "a", "b", "n", where a ≠ 1, b ≠ 1
Loga N= logbN/logbA

### circle

the set of all points in a plane that are equidistant from a given point in the plane, called the center

### Combined variation

when one quantity varies directly and/ or inversely as two or more other quantities

### common difference

the difference between the successive terms of an arithmetic sequence

### common logarithm

logarithms that use 10 as the base

### common ratio

the ratio of successive terms of a geometric sequence

### completing the square

a process used to make a quadratic expression into a perfect square trinomial

### complex conjugates

two complex numbers of the form a+bi and a-bi

### complex fraction

a rational expression whose numerator and/ or denominator contains a rational expression

### 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

### 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)].

### compound inequality

two inequalities joined by the word "and" or "or"

### conic section

any figure that can be obtained by slicing a double cone

### consistent

a system of equation that has at least one solution

### constant of variation

the constant k used with direct or inverse variation

### continuous relation

a relation that can be graphed with a line or smooth curve

### correlation coefficient

a measure that shows how well data are modeled by a linear equation

### dependent

when a system of linear equations has an infinite number of solutions

### dimensions of a matrix

the number of rows, m, and the number of columns, n, of the matrix written as m x n

### 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

### discriminant

in the quadratic formula, the expression b^2 -4ac

### 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

### end behavior

the behavior of the graph as x approaches positive infinity or negative infinity

### exponential equation

an equation in which the variables occur as exponents

### extraneous solution

a number that does not satisfy the original equation

### extrema

the max and min values of a function

### factor theorem

the binomial x-r is a factor of the polynomial P(x) if and only if P(r)=0

### Finite sequence

a sequence containing a limited number of terms

### function

a relation in which each element of the domain is paired with exactly one element in the range

### 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

### greatest integer function

a step function, written as f(x)=[[x]], where f(x) is the greatest integer less than or equal to x

### growth factor

in exponential growth, the base of the exponential expression, 1+r

### 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

### identity function

the function I(x)=x

### imaginary unit

i, or the principal square root of -1

### inconsistent

a system of equations that has no solutions

### independent

when a system of linear equations has exactly one solution

### infinite sequence

a sequence that continues without end

### interval notation

a way to describe the solution set of an inequality

### inverse function

two functions f and g are inverse functions iff both of their compositions are the identity function

### inverse relation

two relations are inverse relations iff whenever one relation contains the element (a,b) the other relation contains the element (b,a)

### 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

### joint variation

y varies jointly as x and z if there is some nonzero contant k such that y=kxz

### latus rectum

the line segment through the focus of a parabola and perpendicular to the axis of symmetry

### linear programming

the process of finding the max or min values of a function for a region defined by inequalities

### 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"

### 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.

### matrix

any rectangular array of variables or contants in horizontal rows and vertical columns

### 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

### natural logarithm

logarithms with base e written lnx

### negative exponent

for any real number a≠0 and any integer n, a^-n= 1/a^n and 1/a^-n= a^n

### 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

### parent function

the simplest most general function in a family of function

### piece wise defined function

a function that is written using two or more expressions

### 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

a function described by the equation f(x)= ax^2 +bx+c where a≠0

in nth roots the value inside in the symbol √(n). Indicates the value that is being taken to the nth root

### rate of change

how much a quantity changes on average relative to the change in another quantity over time

### rational exponent

for any nonzero real number b, and any integers m and n, with

except when b<0 and n is even

### 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

### rationalizing the denominator

to eliminate radicals from a denominator or fractions from a radicand

### recursive formula

each term is formulated from one or more previous terms

### regression line

a line of best fit

### relative maximum

a point on the graph of a function where no other nearby points have a greater y coordinate

### relative minimum

a point on the graph of a function where no other nearby points have a lesser y coordinate

### root

the solutions of a quadratic equation

### scatter plot

a set of data graphed as ordered pairs in a coordinate plane

### sequence

a list of numbers in a particular order

### set builder notation

the expression of the solution set of an inequality for example {xlx>0}

### step function

a function whose graph is a series of line segments

### synthetic division

a method used to divide a polynomial by a binomial

### 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

### vertical line test

if no vertical line intersects a graph in more than one point then the graph represents a function

### zeros

the x intercepts of the graph of a function the points for which f(x) =0