Algebra II

The Distributive Property of Multiplication and Division Over Addition and Subtraction

c (a ± b) = c * a ± c * b and a ± b / c = a/c ± b/c

Like Terms

Two or more terms that have the same variables raised to the same powers. In like terms, only the coefficients (the numbers multiplying the variables) can differ.

Linear Equations

An equation between two variables that gives a straight line when plotted on a graph.

The Associative Properties of Addition and Multiplication

(a + b) + c = a + (b + c) and (a * b) * c = a * (b * c)

Expression

A combination of terms using addition and subtraction.

Continuous function

A function for which sufficiently small changes in the input result in arbitrarily small changes in the output. Otherwise, a function is said to be a discontinuous function.

Variable

A quantity that is unknown, unspecified, or can change within the context of a problem. Most often, variables are represented by a letter or a symbol.

Direct Variation

A relationship between two variables in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first. If b is directly proportional to a, the equation is of the form b = ka (where k is a constant).

Terms

A single number or combination of numbers and variables using exclusively multiplication or division.

Monomials

An algebraic expression consisting of one term.

Binomials

An algebraic expression of the sum or the difference of two terms.

Function

Any "rule" that assigns exactly one output value (y-value) for each input value (x-value). These rules can be expressed in different ways, the most common being equations, graphs, and tables of values. We call the input variable INDEPENDENT and the output variable DEPENDENT.

Algebraic Expressions

Combinations of constants and variables using the typical operations of addition, subtraction, multiplication, and division along with exponents and roots (square roots, cube roots, etc.)

Polynomials

Expressions that are mainly combinations of terms with both addition and subtraction that can have only constants and positive integer powers. They are truly just an extension of our base-10 number system.

Repeated Multiplication

Raising to powers by repeated multiplication. The result of raising a number (the base) to a power (the exponent) is the same number that would be obtained by multiplying the base number together the number of times that is equal to the exponent.

Composition of Functions

Since functions convert the value of an input variable into the value of a output variable, it stands to reason that this output could then be used as an input to a second function. This process is known as COMPOSITION OF FUNCTIONS, in other words, combining the actions or rules of two functions.

Proportional or Direct Relationships

Two variables, x and y, have a DIRECT (PROPORTIONAL) RELATIONSHIP if for every ordered pair (x and y) we have: y/x = k or y = kx y will always be a constant multiple of x. The value of k is known as the CONSTANT OF VARIATION

The Commutative Properties of Addition and Multiplication

a + b = b + a and a * b = b * a

Function Notation

y = f (x) Output ^ ^Input