Math Chapter (3)

Function Rule

A function can be defined by any mathematical condition relating each argument (input value) to the corresponding output value. If the domain is finite, a function f may be defined by simply tabulating all the arguments x and their corresponding function values f(x).

Coefficient

A number or symbol multiplied with a variable or an unknown quantity in an algebraic term. For example, 4 is the coefficient in the term 4x, and x is the coefficient in x(a + b). A numerical measure of a physical or chemical property that is constant for a system under specified conditions

Numerical Expression

A numerical expression is a mathematical phrase involving only numbers and one or more operational symbols. Examples of Numerical Expression. The following are some examples of numerical expressions.

Powers

A power is the product of multiplying a number by itself. Usually, a power is represented with a base number and an exponent. The base number tells what number is being multiplied. The exponent, a small number written above and to the right of the base number, tells how many times the base number is being multiplied.

Arithmetic Sequence

A sequence is an ordered list of numbers and the sum of the terms of a sequence is a series. In an arithmetic sequence, each term is equal to the previous term, plus (or minus) a constant. The constant is called the common difference (d).

Defining the Variable

A symbol for a number we don't know yet. It is usually a letter like x or y. Example: in x + 2 = 6, x is the variable. See: Constant. Algebra - Definitions.

Algebraic Expression

An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add,subtract,multiply, and divide). Here are some algebraic expressions: a + 1. a - b. 3x.

Exponet

An exponent is a small number written with another big number that tells how many times to multiply the big number by itself. It looks like this: 3. and this means 3 x 3 which equals 9.

Equivalent Expression

Equivalent Expressions: Expressions that simplify to an equal value when numbers are substituted for the variables of the expression. For example, (a+b)2 and a2 + 2ab + b2 are equivalent since whatever the numbers you substitute for a and b, you can always get the same value for both expressions.

Factors

Factors are numbers you can multiply together to get another number: Example: 2 and 3 are factors of 6, because 2 × 3 = 6. 3 and 4 are factors of 12, because 3 × 4 = 12. Also 2 × 6 = 12 so 2 and 6 are also factors of 12.

Term

In Algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs. See: Variable. Algebra - Definitions.

Order of Operations

In mathematics and computer programming, the order of operations (or operator precedence) is a collection of rules that define which procedures to perform first in order to evaluate a given mathematical expression. For example, in mathematics and most computer languages, multiplication precedes addition.

Base

In mathematics, a base or radix is the number of different digits or combination of digits and letters that a system of counting uses to represent numbers. For example, the most common base used today is the decimal system.

Sequence

In mathematics, a sequence is an ordered collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence.

Radical Sign

In mathematics: An nth root. A radical expression involving roots. The radical symbol (√), used to indicate the square root and other roots.

Function

In modern mathematics, a function is defined by its set of inputs, called the domain; a set containing the set of outputs, and possibly additional elements, as members, called its codomain; and the set of all input-output pairs, called its graph.

Solution

Mathematics A value or values which, when substituted for a variable in an equation, make the equation true. For example, the solutions to the equation x2 = 4 are 2 and -2.

Equation

Mathematics A written statement indicating the equality of two expressions. It consists of a sequence of symbols that is split into left and right sides joined by an equal sign. For example, 2 + 3 + 5 = 10 is an equation.

Range

The difference between the lowest and highest values. In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9, so the range is 9 − 3 = 6. Range can also mean all the output values of a function. See: Range of a function.

Domain

The domain of a function is the complete set of possible values of the independent variable. In plain English, this definition means: The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

Square Root

The square root of a number is a value that, when multiplied by itself, gives the number. Example: 4 × 4 = 16, so a square root of 16 is 4. Note that (−4) × (−4) = 16 too, so −4 is also a square root of 16. The symbol is √ which always means the positive square root.

Evaluate

To evaluate is to find the value of a numerical or algebraic expression.

Variable

Variable definition. A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters $x$, $y$, and $z$ are common generic symbols used for variables.

Algebra

the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

Square

the product of a number multiplied by itself.

Perfect Square

the product of a rational number multiplied by itself. the product of a polynomial multiplied by itself.