Spring Final Review Flashcards
Arithmetic Sequence
A sequence in wich each term increases by adding/ subtracting k
Asymtote
A line that a graph approaches but does not hit
Change of base formula
A formula that allows you to rewrite a logarithm in terms of logs written with another base
Circle
A shape that consists of points equidistant from the center
Combined variation
Combined variation describes 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 a base 10
Common ratio
The constant ratio r between consecutive terms of a geometric sequence
Completing the square
a c to the form x^2 + bx to make x^2 + bx + c is a perfect square trinomial
Complex conjugates
Pairs of complex numbers of the forms a + bi and a - bi where b == 0
Complex fraction
A fraction made of fractions
Complex number
A number written in the form a + bi where a and b are real numbers
Composition of a fraction
An operation that can be performed with two functions
Compound inequality
an inequality that combines two simple inequalities
Conic section
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.
Consistant
a linear or nonlinear system of equations with at least one set of values for the unknowns that satisfies each equation in the system
Constant of variation
th constant a in the inverse equation y = a/x where a == 0
Continuous relation
the values belonging to the set can take on ANY value within a finite or infinite interval
Correlation coefficient
A number r from -1 to 1 that measures how well a line fits a set of data pairs
Dependent
the variable 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 x n
Direct variation
y increases as x increases
Discriminant
the expression b^2 - 4ac in the quadratic equation
Ellipse
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 of negative infinity
Exponential equation
equations in which variable expressions occur as exponents
Extraneous solutions
Solutions that are not solutions of the original equation
Extrema
the maximum or minimum value of a function
Factor theorem
a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial f(x) has a factor if and only if f(k)=0
Finite sequence
has a limited number of terms and infinite if it does not
Function
a binary relation between two sets that associates to each element of the first set exactly one element of the second set. Typical examples are functions from integers to integers, or from the real numbers to real numbers
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
Growth factor
the value of b in an exponential growth function of the form y = ab^x, where a > 0 and b > 1
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. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows
Identity function
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
inconsistant
a system that has no solution
independent
a variable that represents a quantity that is being manipulated in an experiment. A dependent variable represents a quantity whose value depends on those manipulations
Infinite sequence
a sequence with no end
Interval notation
a set of real numbers that contains all real numbers lying between any two numbers of a set
Inverse function
a function that “reverses” another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, i.e., g(y) = x if and only if f(x) = y. The inverse function of f is also denoted as f^{-1}
Inverse relation
the value of one parameter tends to decrease as the value of the other parameter in the relationship increases. It is often described as a negative relationship
Inverse variation
mathematical relationship between two variables which can be expressed by an equation in which the product of two variables is equal to a constant
Joint variation
a variable varies directly or inversely with multiple variables. For instance, if x varies directly with both y and z, we have x = kyz
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
a mathematical technique for maximizing or minimizing a linear function of several variables, such as output or cost
Logarithm
a quantity representing the power to which a fixed number (the base) must be raised to produce a given number
Logistic growth model
a common S-shaped curve with equation {\displaystyle f(x)={\frac {L}{1+e^{-k}}}, } where x_{0}, the x value of the sigmoid’s midpoint; L, the curve’s maximum value; k, the logistic growth rate or steepness of the curve
Matrix
a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. For example, the dimension of the matrix below is 2 × 3, because there are two rows and three columns
n^th root
for an integer n greater than 1, if b^n=a, then b is an n^th root of a
Natural logarithm
a logarithm with base e, denoted by log\/e or in
Negative exponent
how many times to divide by the number
Parabola
the graph of a quadratic function
Parent function
the most basic function in a famiy of functions
Piece-wise defined function
a function defined by two or more equations
Point-slope form
y − y1 = m(x − x1)
Quadratic function
a function that can be written in the form f(x)=a(x-h)^2+k where a == 0
Radicand
The value inside the radical symbol
Rate of change
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 with the form y=p(x)/q(x)
Rationaizing the denominator
to eliminate any radical expressions in the denominator such as square roots and cube roots
Recursive formula
a formula that defines each term of a sequence using preceding term(s). Recursive formulas must always state the initial term, or terms, of the sequence
Regression line
a line that best describes the behavior of a set of data
Relative maximum
a point that is higher than the points directly beside it on both sides
Relative minimum
a point that is lower than the points directly beside it on both sides
Root
a solution of an equation
Scatter plot
a graph in which the values of two variables are plotted along two axes, the pattern of the resulting points revealing any correlation present
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 piecewise function defined by a constant value over each part of its domain
Synthetic devision
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
Vertical line test
a method that is used to determine whether a given relation is a function or not
Zeros
x intercepts of the graph of the function the points for which f(x)=0
