Function -- a relation of variables x and y, where each input has only one output.  Can be written in many forms, include "Slope Intercept Form", "y = 3x +1", or "Function Form", "f(x) = 3x +1".

Examples:
(3,4) (4,5) (7,12) (10, 14)
Non-Examples:
(3,4) (3,5) (3,12) (3, 14)

Domain -- all of the input values (or x-values) in a function.


Range -- all of the output values (or y-values) in a function.


Linear Function -- a function that makes a straight line of any slope (cannot be vertical).  Identified by a function that has x to the power of 1 in its name.

Examples:

y = x

y = 2x

y = -5x + 7


Quadratic Function -- a function that makes a parabola (U-shape) that opens upward or downward.  Identified by a function that has x to the power of 2 in its name.

Examples:

y = x2

y = 2x2

y = -5x2 + 7

Cubic Function -- a function that makes a cubic curve (sideways S-shape) that opens upward or downward.  Identified by a function that has x to the power of 2 in its name.

Examples:

y = x2

y = 2x2

y = -5x2 + 7


Expression -- a math sentence that may or may not have variables in it.

Example:  13 - 4 + 7


Algebraic Expression -- a math sentence that has variables in it.

Example: 8x + 2 - y


Coefficient-- the number attached to a variable.

Example: In the equation 8x + 2 = 12 , "8" is the coefficient.


Constant Term-- a regular number in an equation or expression whose value never changes.

Example: In the equation 8x + 2 = 12 , "2" and "12" are both constant terms.


Variable -- a letter that represents a missing number in an expression.

Example: In the equation 8x + 2 = 12 , "x" is a variable.


Variable Term-- a piece of a math sentence that has a variable (letter) in it.

Example: In the equation 8x + 2 = 12 , "8x" is a variable term.


Equation-- two equal expressions.

Examples:

8 + y = 14 (algebraic equation)

5 + 2 = 3 + 4 (numeric equation)


Inequality-- two expressions that are NOT equal.  Solutions must be shown using a number line or graph because there may be multiple answers.

Example: 4x + 3 < 24


Associative Property-- you can change the numbers in a group when multiplying or adding without changing the value of the expression.

Example:

4 + (5 + 6) = (4 + 5) + 6   ---> Associative Property of Addition

a(bc) = (ab)c   ---> Associative Property of Multiplication


Commutative Property-- you can add or multiply numbers in any order.

Examples:

(4)(5)(2) = (2)(5)(4)  ---> Commutative Property of Multiplication

a + b + c = c + a + b  ---> Commutative Property of Addition


Distributive Property-- you can break down numbers and represent them in different ways using multiplication; a number or value on the outside of parentheses must be shared by multiplication with every term inside the parentheses.

Examples:

2(483) = 2(400) + 2(80) + 2(3)

4(a + b) = 4a + 4b


Identity Property of Addition-- you can add zero to any number or variable without changing its value.

Examples:
a + 0 = a
14 + 0 = 14


Identity Property of Multiplication-- you can multiply any number or variable by 1 without changing its value.

Examples:
a x 1 = a
(14)(1) = 14


Additive Inverse Property-- any number added to its opposite will equal zero.

Examples:
a + (-a) = 0
-14 + 14 = 0

Multiplicative Inverse Property-- any number multiplied by its reciprocal will equal 1.
Examples:
2 x 1/2 = 1
2/3 x 3/2 = 1


Operations-- The four processes in mathematics: addition, subtraction, multiplication, and division.


Inverse Operations -- opposite operations that undo one another.

Example: Addition and subtraction are inverse operations because they undo one another.

 

Integers -- (a family of numbers) all positive and negative whole numbers and zero.

{...-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7...}


Rational Numbers-- all whole numbers, fractions, terminating or repeating decimals, integers, or the square root of a perfect square number.

Examples: The square root of 16, the number -8, or the fraction two-thirds.


Irrational Numbers-- any number that cannot be expressed in faction form; decimals that never terminate and never repeat, or any square root of a non-perfect square number.

Examples: the square root of 7 or Pi

Absolute Value-- the distance a number is from zero. *IT CAN NEVER BE NEGATIVE!*

Examples:

I 5 I = 5, because positive 5 is five places away from zero.

I -5 I = 5, because positive -5 is five places away from zero.


Factoring -- dividing.


Prime Factoring-- dividing a number using only prime numbers.
Example: The prime factorization of 40 = 2 x 2 x 2 x 5

Prime Number-- a number that can only be dividing by 1 and itself.
{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47...}


Composite Number -- a number that has more factors than just 1 and itself.

Example: The number 20 is "composite" because it can be divided by 1 and 20, but also 2, 4, 5, and 10.

Sum -- the answer to an addition problem.

"The SUM of 9 and a number" is written "9 + x".


Difference-- the answer to a subtraction problem.

"The DIFFERENCE of 9 and a number" is written "9 - x".


Product -- the answer to a multiplication problem.

"The PRODUCT of 9 and a number" is written "9x".


Quotient -- the answer to a division problem. 

"The QUOTIENT of 9 and a number" is written " 9 "

                                                                      x