arithmetic sequence

a linear function with a domain of positive consecutive integers in which the difference between any two consecutive range terms is equal

asymptote

a line that an exponential graph gets closer and closer to, but never crosses or touches

common difference

the number added to each consecutive term in an arithmetic sequence

continuous

having no breaks

curve

the graphical representation of the solution set for y = f(x); in the special case of a linear equation, it will be a line

dependent variable

the output variable of a function

discrete

individually separate and distinct

domain

the set of all inputs of a function; the set of x-values that are valid for the function

end behavior

the behavior of the graph as x becomes larger or smaller

equation

a mathematical sentence that uses an equal sign (=) to show that two quantities are equal

explicit equation

an equation used to find the nth term of a sequence; some examples are a_{n} = a_{1} + (n – 1)d and a_{n} = a_{1} • r _{n – 1}

exponential function

a function that has a variable in the exponent; the general form is f(x) = ab^{x}, where a is the initial value, b is the rate of decay or growth, x is the time, and f(x) is the final output value

expression

a combination of variables, quantities, and mathematical operations; 4, 8x, and b + 102 are all examples.

extrema

the minima and maxima of a function

factor

one of two or more numbers or expressions that when multiplied produce a given product

function

a relation in which every element of the domain is paired with exactly one element of the range; that is, for every value of x, there is exactly one value of y.

function notation

a way to name a function using f(x) instead of y

geometric sequence

an exponential function that results in a sequence of numbers separated by a constant ratio

growth factor

the number multiplied by each consecutive term in a geometric sequence, also known as the constant ratio

growth rate

the growth factor minus 1

independent variable

the input variable of a function

integer

a number that is not a fraction or a decimal

irrational numbers

numbers that **cannot **be written as a/b, where a and b are integers and b ≠ 0; any number that cannot be written as a decimal that ends or repeats

linear equation

an equation that can be written in the form ax + by = c, where a, b, and c are rational numbers; can also be written as y = mx + b.

linear function

a function that can be written in the form f(x)=mx + b, in which m is the slope, b is the y-intercept, and the graph is a line

natural numbers

the set of positive integers {1, 2, 3, ..., n}

ordered pair

a pair of values (x, y) where the order is significant

range

the set of all outputs of a function; the set of y-values that are valid for the function

rate of change

a ratio that describes how much one quantity changes with respect to the change in another quantity; also known as the slope of a line

rational numbers

a number that **can** be written as a/b , where a and b are integers and b ≠ 0; any number that can be written as a decimal that ends or repeats