Algebra 2 final Flashcards
arithmetic sequence
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 2-dimensional shape made by drawing a curve that is always the same distance from a center.
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 between consecutive terms of an arithmetic sequence
common logarithm
the logarithm with base 10
common ratio
The constant factor between consecutive terms of a geometric sequence
completing the square
A method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial .
complex conjugates
The complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.
complex fraction
A fraction in which numerator, denominator, or both are themselves fractions.
Complex number
A combination of a real and an imaginary number in the form a + bi
Composition of fractions
Combining functions to make another function.
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;
Consistent
If a system has at least one solution.
Constant of variation
The constant of variation is the number that relates two variables that are directly proportional or inversely proportional to one another.
Continuous relation
A function for which sufficiently small changes in the input result in small changes in the output.
Correlation coefficient
a number between −1 and +1 calculated so as to represent the linear dependence of two variables or sets of data.
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 are the number of rows by the number of columns.
Direct variation
Direct variation describes a simple relationship between two variables .
Discriminate
A relatively simple expression that determines some of the properties, as the nature of the roots, of a given equation or function.
Ellipse
An ellipse is the set of all points on a plane whose distance from two fixed points F and G add up to a constant.
end behavior
looking at the two extremes of x. As x gets closer to infinity and as x gets closer to negative infinity
exponential equation
an equation involving exponential functions of a variable.
extraneous solution
a root of a transformed equation that is not a root of the original equation
extrema
the maximum or minimum value of a function.
factor theorem
a theorem linking factors and zeros of a polynomial
finite sequence
has a limited number of terms and infinite if it does not
function
a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
geometric sequence
A sequence made by multiplying by the same value each time.
greatest integer function
a function that returns a constant value for each specific interval
growth factor
the factor by which a quantity multiplies itself over time
hyperbole
is two curves that are like infinite bows
identity function
a function which returns the same value, which was used as its argument.
imaginary unit
A number that when squared gives a negative result.
inconsistent
When you graph the equations, both equations represent the same line.
independant
a 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 integer
interval notation
a way of writing subsets of the real number line
inverse function
a function that undoes the action of the another function
inverse relation
the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function
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
occurs when a variable varies directly or inversely with multiple variables.
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.
lagistic growth model
a population’s per capita growth rate gets smaller and smaller as population size approaches a maximum imposed by limited resources in the environment, known as the carrying capacity
matrix
rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.
n root
n times in a multiplication to get the original value.
natural logarithm
logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately equal to 2.718281828459
negative exponent
how many times to divide by the number.
parabola
a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side.
parent function
the simplest form of a given family of functions.
piece-wise defined function
one which is defined not by a single equation, but by two or more.
point-slope form
the equation of a straight line in the form y − y1 = m(x − x1) where m is the slope of the line and (x1, y1) are the coordinates of a given point on the line — compare slope-intercept
quadratic function
a polynomial function with one or more variables in which the highest-degree term is of the second degree.
radicand
The value inside the radical symbol
rate of change
the speed at which a variable changes over a specific period of time.
rational exponent
an exponent that is a fraction
rational function
A function that is the ratio of two polynomials.
rationalizing 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
regression line
a straight line that describes how a response variable y changes as an explanatory variable x changes.
relative maximum
a point where the function changes direction from increasing to decreasing
relative minimum
all the points x, in the domain of the function, such that it is the smallest value for some neighborhood
root
Where a function equals zero.
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
A list of numbers or objects in a special order
set-builder notation
How to describe a set by saying what properties its members have
step function
a function that increases or decreases abruptly from one constant value to another.
synthetic division
a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division.
vertex form
a point where two or more curves, lines, or edges meet.
vertical line test
a method that is used to determine whether a given relation is a function or not.
zeros
Where a function equals the value zero
