spring semester final Flashcards by Brynn Daniel

A sequence in which the difference of consecutive terms is constant

Arithmetic sequence

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A line that a graph approaches more and more closely

Asymptote

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log c (a) = log b (a) / log b (c)

Change of base formula

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A round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center)

Circle

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Varies directly with some of them and varies inversely with others

Combined variation

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The constant difference d between consecutive terms of an arithmetic sequence

Common difference

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A logarithm with base 10, denoted as log 10 or simply by log

Common logarithm

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The constant ratio r between succesive terms of a geometric sequence

Common ratio

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To add a term c to am expression of the form x^2 + bx such that x^2 + bx + c is a perfect square trinomial

Completing the square

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Pairs of complex numbers of the forms a + bi and a - bi, where b does not equal zero

Complex conjugates

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A fraction that contains a fraction in its numerator or denominator

Complex fraction

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A number written in the form a + bi, where a and b are real numbers

Complex number

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An operation that can be performed with two functions

Composition of functions

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An inequality that combines two simple inequalities

Compound inequality

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A curve obtained as the intersection of the surface of a cone with a plane

Conic section

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A linear or nonlinear system of equations that has at least one solution (constant)

Consistent

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The constant a in the in the inverse variation equation y= a/x , where a does not equal 0

Constant of variation

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All reals domain and range

Continuous relation

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A number from -1 to 1 that measures how well a line fits a set of data pairs (x,y)

Correlation coefficient

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Variable that depends on the value of some other number that has infinite solutions

Dependent

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The dimensions of a matrix with m rows and columns are m X n

Dimensions of a matrix

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A simple relationship between two variables in which y=xk or y/x=k

Direct variation

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The expression b^2 - 4ac in the Quadratic Formula

Discriminant

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A plane curve surrounding two focal points

Ellipse

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The behavior of the graph of a function as x approaches positive infinity or negative infinity

End behavior

Equations in which variable expressions occur as exponents

Exponential equation

Solutions that are not solutions of the original equation

Extraneous solution

Any point at which the value of the function is at the largest (maximum) or smallest (minimum)

Extrema

A theorem linking factors and zeros of a polynomial

Factor theorem

Term following a sequence that has a definite end and beginning 2,4,6

Finite sequence

A binary relation between two sets that associates to each element of the first set exactly one element of the second set

Function

A sequence in which the ratio of any term to the previous term is constant

Geometric sequence

A step function that returns a constant value for each specific interval. llxll

Greatest integer function

The value of b in an exponential growth function of the form y=ab^x, were a > 0 and b > 1

Growth factor

A type of smooth curve lying in a plane, defined by its geometric properties

Hyperbola

A function that always returns the same value that was used as its argument

Identity function

Imaginary number . The square root of -1

Imaginary unit

If it consists of a contradiction

Inconsistent

Does not depend on another variable

Independant

Term following a sequence that goes on forever

Infinite sequence

A way to describe the solution set of n inequality

Interval notation

Functions that undo each other

Inverse function

The set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function (a,b) (b,a)

Inverse relation

Two variables x and y show inverse variation when y=k/x or yx=k

Inverse variation

Occurs when a variable varies directly or inversely with multiple variables. y=kxz or y/xz=k

Joint variation

The chord (line segment) that passes through the focus, is perpendicular to the major axis and has both endpoints on the curve.

Latus rectum

The process of finding the maximum or minimum values of a function for a region defined by inequalities

Linear programming

The exponent to which another fixed number, the base b, must be raised, to produce that number x. log base. limits growth

Logarithm

A common S-shaped curve in a log model

Logistic growth model

A rectangular arrangement of numbers

Matrix

It is the "radical" symbol (used for square roots) with a little n

nth root

A logarithm with base e, denoted by log e or base n

Natural logarithm

The sign on an exponent that means the reciprocal. moves exponent

Negative exponent

The graph of a quadratic formula

Parabola

The most basic function in a family of functions

Parent function

A function defined by two or more equations

Piece-wise defined function

The equation of a straight line in the form y − y1 = m(x − x1)

Point-slope form

A function that can be written in the form f(x)=a(x-h)^2 = k, where x cannot equal 0

Quadratic function

The value inside the radical symbol

Radicand

Used to mathematically describe the percentage change in value over a defined period of time

Rate of change

A number such as −3/7 that can be expressed as an integer or fraction

Rational exponent

Any function which can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials

Rational function

To eliminate any radical expressions in the denominator such as square roots and cube roots

Rationalizing the denominator

A formula that defines each term of a sequence using preceding term(s)

Recursive formula

An estimate of the line that describes the behavior of a set of data

Regression line

A point where the function changes direction from increasing to decreasing (making that point a "peak" in the graph

Relative maximum

The lowest point a particular section of a graph

Relative minimum

A solution to a function, x=0

Root

A set of data graphed as ordered pairs in a coordinate

Scatter plot

An ordered list of numbers

Sequence

Uses symbols to define a set, in terms of the properties of the members of the set. xlx

Set-builder notation

A piecewise function defined by a constant value over each part of its domain

Step function

A shortcut method to divide a polynomial by a binomial of the form x - k

Synthetic division

A quadratic function written in the form f(x)= a(x-h)^2 + k, where a does not equal 0

Vertex form

A visual way to determine if a curve is a graph of a function or not

Verticle line test

Where a function equals the value 0

Zeros