Vocab Final Flashcards
Arithmetic sequence
A sequence in which the difference of consecutive terms is constant
Asymptote
A line that a graph approaches more and more closely
Change of Base Formula
A formula that allows you to rewrite a logarithm in terms of logs written with another base. This is especially helpful when using a calculator to evaluate a log to any base other than 10 or e.
Circle
a polygon that has no corners and is a full 360
Combined Variation
a situation where a variable depends on two (or more) other variables, and varies directly with some of them and varies inversely with others (when the rest of the variables are held constant).
Common Difference
The constant difference d between consecutive terms of an arithmetic sequence
Common Logarithm
A logarithm with base 10. denoted as log10 or simply log
Common Ratio
The constant ratio r between consecutive terms of a geometric sequence
Completing the Square
To add a term c to an expression of the form x^2 + bx such that
x^2 + bx + c is a perfect square trinomial
Complex Conjugates
Pairs of complex numbers of the forms a +bi, where b =/= 0
Complex Fraction
A fraction that contains a fraction in its numerator or denominator
Complex Number
A number written in the form a + bi, where a and b are real numbers
Composition of Fractions
An operation that can be performed with two numbers
Compound Inequality
is an inequality that combines two simple inequalities.
Conic Section
In mathematics, a conic section is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type.
Consistent
In mathematics and particularly in algebra, a linear or nonlinear system of equations is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system—that is, when substituted into each of the equations, they make each equation hold true as an identity.
Constant of Variation
The constant a in the inverse variation equation y= a/x, where a =/= 0
Continuous Relation
A set of data is said to be continuous if the values belonging to the set can take on ANY value within a finite or infinite interval. Definition: A set of data is said to be discrete if the values belonging to the set are distinct and separate (unconnected values).
Correlation Coefficient
A number r from -1 to 1 that measures how well a line fits a set of data pairs (x,y)
Dependent
a variable that relies on another variable usually the independent variable
Dimensions of a Matrix
The dimensions of a matrix with m rows and n columns are m X n
(read “m by n”)
Direct Variation
a simple relationship between two variables . We say y varies directly with x (or as x , in some textbooks) if: y=kx. for some constant k , called the constant of variation or constant of proportionality .
Discriminant
The expression b^2 - 4ac in the Quadratic Formula
Ellipse
In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. As such, it generalizes a circle, which is the special type of ellipse in which the two focal points are the same.
End Behavior
The behavior of the graph of a function as x approaches positive infinity or negative infinity
Exponential Equation
Equations in which variable expressions occur as exponents
Extraneous Solution
Solutions that are not solutions of the original equation
Extrema
Any point at which the value of a function is largest (a maximum) or smallest (a minimum).
Factor Theorem
Used when factoring polynomials “completely”
Finite Sequence
The differences of consecutive y-values in a data set when the x-values are equally spaced
Function
a relationship or expression involving one or more variables.
Geometric Sequence
A sequence in which the ratio of any term to the previous term is constant
Greatest integer Function
The function rounds -off the real number down to the integer less than the number. This function is also known as the Floor Function.
Growth Factor
The value of b in an exponential growth function of the form y = ab^x, where a>0 and b>1
Hyperbola
In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.
Identity Function
In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument. That is, for f being identity, the equality f(x) = x holds for all x.
Imaginary Unit
The square root of -1, denoted i = sqrt(-1)
Inconsistent
When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
Independent
a variable that doesn’t depend on anything else
Infinite Sequence
a list or string of discrete objects, usually numbers, that can be paired off one-to-one with the set of positive integer s {1, 2, 3, …}. … An infinite series is the sum of the values in an infinite sequence of numbers.
Interval Notation
In mathematics, a interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between.
Inverse Function
Functions that undo each other
Inverse Relation
The set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function. If the graph of a function contains a point (a, b), then the graph of the inverse relation of this function contains the point (b, a).
Inverse Variation
Two variables x and y show inverse variation when
y = a/x, where a =/= 0
Joint Variation
describes a situation where one variable depends on two (or more) other variables, and varies directly as each of them when the others are held constant. We say z varies jointly as x and y if. z=kxy. for some constant k.
Latus Rectum
a chord of a conic section (such as an ellipse) that passes through a focus and is parallel to the directrix
Linear Programming
mathematical modeling technique in which a linear function is maximized or minimized when subjected to various constraints. This technique has been useful for guiding quantitative decisions in business planning, in industrial engineering, and—to a lesser extent—in the social and physical sciences.
Logarithm
a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
Logistic Growth Model
f(x) = L/1+ e^{-k(x-x>0)} a common S-shaped curve with equation the x value of the sigmoid’s midpoint; L, the curve’s maximum value; k, the logistic growth rate or steepness of the curve.
Martix
A rectangular arrangement of numbers
Nth Root
For an integer n greater than 1, if b^n = a, then b is an nth root of a.
Natural Logarithm
A logarithm with the base e. denoted by log>e or ln
Negative Exponent
6^-x = 1/6^x how many times to divide by the number. exponential grows
Parabola
The graph of a quadratic function
Parent Function
The most basic function in a family of functions
Piece-Wise Defined Function
A function defined by two or more equations
Point-Slope Form
The equation of a straight line in the form y − y>1 = m(x − x>1) where m is the slope of the line and (x>1, y>1) are the coordinates of a given point on the line
Quadratic Function
A function that can be written in the form f(x) = a(x - h)^2 + k, where a =/= 0
Radicand
A number or expression inside the radical symbol
Rate of Change
used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable.
Rational Exponent
an exponent that is a fraction.
Rational Function
A function that has the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomials and q(x) =/= 0
Rationalizing the Denominator
to eliminate any radical expressions in the denominator such as square roots and cube roots. The key idea is to multiply the original fraction by an appropriate value, such that after simplification, the denominator no longer contains radicals.
Recursive Formula
formula that defines each term of a sequence using preceding term(s).
Regression Line
an estimate of the line that describes the true, but unknown, linear relationship between the two variables. The equation is used to predict (or estimate) the value of the response variable from a given value of the explanatory variable.
Relative Maximum
a point where the function changes direction from increasing to decreasing
Relative Minimum
point where the function changes direction from decreasing to increasing
Root
A solution of an equation or think square root
Scatter Plot
a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. lots of dots can find line of best fit
Sequence
An ordered list of numbers
Set-Builder Notation
Uses symbols to define a set, in terms of the properties of the members of the set.
Step Function
A piece wise function defined by a constant value over each part of its domain
Synthetic Division
A shortcut method to divide a polynomial by a binomial of the form x - k
Vertex Form
A quadratic function written in the form f(x) = a(x - h)^2 + k, where a =/= 0
Vertical Line Test
drawing a vertical line on a graph to see if there are two points on a single part of the x axis to determine if it is a function or not
Zeros
A x-value of a function f for which f(x) = 0
