Spring Finals Review Flashcards
Arithmetic Sequence
Each term increases by adding/subtracting some constant k
Asymptote
A line that continually approaches a given curve
Change of Base Formula
logb(a) = logx(a)/logx(b)
Circle
A round plane figure
Combined Variation
A variable depends on two (or more) other variables, and varies directly with some of them and varies inversely with others
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 by log.
Common Ratio
The constant ratio r between consecutive terms of a geometric sequence
Completing the Square
a technique for converting a quadratic polynomial of the form ax^{2}+bx+c
Complex Conjugates
Pairs of complex numbers of the forms a + bi and a-bi, where b doesn’t equal 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 Functions
An operation that can be formed with 2 functions
Compound Inequality
An inequality that combines two simple inequalities.
Conic Section
A figure formed by the intersection of a plane and a right circular cone
Consistent
A linear or nonlinear system of equations
Constant of Variation
The constant a in the inverse variation equation y = a/x, where a doesn’t equal 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.
Correlation Coefficient
Expressed using the variable r, where r is between 1 and –1, inclusive.
Dependent
The dependent variable is the one that depends on the value of some other number.
Dimensions of a Matrix
The dimensions of a matrix with m rows and n columns are m by n.
Direct Variation
A simple relationship between two variables.
Ellipse
Plane curve surrounding two focal points, such that for all points on the curve (oval).
Exponential Equation
A function of the form y = ab^2, where a doesn’t equal 0, and the base b is a positive real number other than 1.
End Behavior
The behavior of the graph of a function as x approaches +infinity or -infinity
Extraneous Solution
Solutions that are not solutions of the original behavior.
Extrema
The maximum or minimum value of a function.
Factor Theorem
A theorem linking factors and zeros of a polynomial.
Finite Sequence
A list of terms in a specific order.
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
a function that returns a constant value for each specific interval
Growth Factor
The value of b in an exponential growth function of the form y = ab^x, where a>0 and b > 1
Discriminant
The expression b^2 -4ac in the Quadratic Formula
Hyperbola
a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.
Identity Function
the function which assigns every real number to the same real number
Imaginary Unit
The square root of -1, denoted as i
Inconsistent
If a system has no solution
Independent
variable that represents a quantity that is being manipulated in an experiment
Infinite Sequence
a list or string of discrete objects, usually numbers, that can be paired off one-to-one with the set of positive integers
Interval Notation
way of writing subsets of the real number line
Inverse Function
a function that undoes the action of another function
Inverse Relation
the value of one parameter tends to decrease as the value of the other parameter in the relationship increases
Inverse Variation
Two variables x and y show inverse variation when y = a/x, where a doesn’t equal 0
Joint Variation
variable varies directly or inversely with multiple variables.
Latus Rectum
the chord through a focus parallel to the conic section directrix
Linear Programming
technique for maximizing or minimizing a linear function of several variables
Logarithm
quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
Logistic growth Model
common S-shaped curve
Matrix
A rectangular arrangement of numbers
n^th 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 a base e
Negative Exponent
how many times to divide by the numbe
Parabola
Graph of a quadratic function
Parent Function
The most basic function in a family of function
Pieve-wise defined function
function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain
Point-Slope Form
y − y1 = m(x − x1), where m is the slope of the line
Quadratic Function
A function that can be written in t he form f(x) = a(x-h)^2 +k, where a doesn’t equal 0
Radicand
what is inside the root sign
Rate of change
the percentage change in value over a defined period of time
Rational Exponent
the percentage change in value over a defined period of time
Rational Function
A function that has the form f(x) = p(x)/q(x), where p(x) and q(x) are plynomials and q(x) doesn’t equal 0
Rationalizing the Denominator
eliminate any radical expressions in the denominator such as square roots and cube roots
Recursive formula
defines each term of a sequence using the preceding term(s)
Regression line
regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables
Relative Maximum
point where the function changes direction from increasing to decreasing
Relative Minimum
is all the points x, in the domain of the function, such that it is the smallest value for some neighborhood
Root
A solution of an equation
Scatter Plot
a graph in which the values of two variables are plotted along two axes
Sequence
An ordered list of numbers
Set-Builder Notation
describing a set by enumerating its elements, or stating the properties that its members must satisfy
Step Function
a function that increases or decreases abruptly from one constant value to another.
Synthetic Division
A shortcut method to divide a polynomial by a binomial of the x - k
Vertical Line Test
visual way to determine if a curve is a graph of a function or not
Zeros
is a member x of the domain of f such that f(x) vanishes at x
Vertex Form
point where two or more curves, lines, or edges meet
