Mr. Ray Bonnette

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1. Definition

2. Example

3. Examples that vary in difficulty

A. Review Algebra I (Chapter 1-2)

B. Graphing (Chapter 3)

In the basics, it is just a set of Relations.
A relation is just a paring of x and y
x is called the domain.
y is called the range.
So a function is where: only one member of the domain corresponds with only one member of the range.
Test for a function: vertical line test
yes --> vertical line only hits once
not --> vertical line hits more than once
Notation
f(x)-->"f of x"
The symbol can now take the place of "y"
For example y=3x-7 ----> f(x)=3x-7
Evaluating functions
The function is f(x)=2x+3
what ever number you place in the f of x's x will replace every where you see x though out the whole equation.

C. Systems of Equations (Chapter 4)

Parallel lines look like/mean- #not equal# , no solution

Same line- #=#, same number

intersection- (x,y), ordered pairs

Jennifer Baiada

Simplify-

(adding and subtracting)

Solve-

• Get a particular variable by itself
• Your variable must be
1. Positive
2. In the numerator

Evaluate

• You must substitute numbers for your variables
• Follow order of operations (simplify)
• You will get a number (value) for your answer

Exponent- telling you how many times a base multiplies itself 24

Base- the number or variable being raised to a "power"

Pre-requisities (what you need to know before)

1. Basic Math
• Add/subtract/multiply/divide
• Integers
• Decimals + fractions
• Signed numbers
2. Solve---> get a particular variable by itself
• Your variable must be
1. Positive
2. The numerator

Inequalities

• Deals with greater than/ less than
• Greater than or =to/less than or = to
• >,> greater than (equal to)
• <,< less than (equal to)

• Conjunction- uses the word "and"
• -2x < x    and   x<1
• -2  < 1
• Disjunction- uses the word "or"
• x>3 or x<-3

• Types of numbers:
• Natural numbers- counting 1,2,3,4...
• No decimals or fractions
• Whole- all naturals with zero
• No decimals / fractions
• Integers- negative, positive, 0
• No decimals / fractions
• Rational- can be written as a fraction
• With 2 integers but zero can not appear in denominator of the fraction
• Irrational- decimals that are non-terminating or no-repeating

Identity Properties:

• Addition- The Identity property of addtion says that any number plus zero is the number itself.
• Ex. 4+0=4
• Ex. 1000+0=1000.
• Multiplication- The Identity propety of multiplication says that any number times one equals the number itself.
• Ex. 3x1=3
• Ex. 5000x1=5000.

Symmetric Propety:

• The symmetric propety states that you can change the order of the numbers in an equation and it will still have the same answer.
• Ex. 4+1=5 or 1+4=5
• Ex. 4x5=20 or 5x5=20

Reciprocal:

• The reciprocal of a number is the number you will add to the number to equal one. The reciprocal in lame terms also means the flipped fraction.
• Ex. 3+1/3=1
• Ex. 17/1=1/17=1

Absolute Value:

• The absolute value of a number is the number of spaces it is from zero on a number line. Even if the number is a negative number, the absolute value will always be positive.
• Ex. l-3l = 3 (the number is three spaces from zero on the number line.)
• Ex. l-45l= 45 (the number is 45 spaces from zero on the number line.)

Constant:

• The constant is a number that never changes in the eqaution. Or a term with no variable.
• Ex. y=4x+2 - In this eqaution , 2 is the constant. It will never change.
• Ex. x=y+12 - In this eqaution , 12 is the constant. It will never change.

Variable:

• The variable in the eqaution is the term that changes.
• Ex. x+4=8 - In this eqaution, the x is the variable. The x will change when the eqaution is sloved.
• Ex. y+500= 950 -In this eqaution, the y is the variable. It will change to solve the eqaution.

Colleen Sullivan.