ALGEBRAALGEBRA

Chapter 1Chapter 1

1.1 – Evaluating Expressions1.1 – Evaluating Expressions

Evaluate the expression when c = 4.1. 4c 2. 8 3. 15 + c c

EXPONENTSEXPONENTS

xn

Important Rule with ExponentsImportant Rule with Exponents

Anything raised to the zero power is ALWAYS 1.

x0 = 1

220 = 1

2550 = 1

Solve the Following Solve the Following ExponentsExponents

Example 1: 26 = ?

Example 2: 43 = ?

Example 3: 92 = ?

Section 1.2: Order of Section 1.2: Order of OperationsOperations

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Steps for Solving Steps for Solving Order of OperationsOrder of Operations

Step 1: Look for parenthesis and do the operations INSIDE of it first.

Step 2: Evaluate all EXPONENTS.

Step 3: Do all multiplication and/or division from LEFT to RIGHT.

Step 4: Do all addition and/or subtraction from LEFT to RIGHT.

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Example 1:Example 1: 3 + 2 3 + 2 3 + 3 + 55

3 + 6 + 53 + 6 + 5

Example 2:Example 2: 48 48 2 233 3 3 + 5+ 5

48 48 8 8 3 + 5 3 + 5

6 6 3 + 5 3 + 5

18 + 518 + 5

Example 3:Example 3: 4[12 4[12 (6 – (6 – 2)]2)]22

4[12 4[12 4] 4]22

4[3]4[3]22

4[9]4[9]

Example 4:Example 4: 225 5 – 6 – 6 2 2 3 333 – 5 – 5 3 – 3 –

22

2255 – 6 – 6 2 2

32 – 6 32 – 6 2 2

32 – 1232 – 12

3333 – 5 – 5 3 – 2 3 – 2

27 – 5 27 – 5 3 – 2 3 – 2

27 – 15 – 227 – 15 – 2

Section 1.3: Write Section 1.3: Write ExpressionsExpressions

Add Subtract Multiply Divide

More Than

Sum

Increased

And

Total

Plus

Less Than

Decreased

Difference

Minus

Product

Times

Of

Quotient

Find some other words that mean the same as the

underlined words.

Example 1: Eight more than a number n.

8 + n

Example 2: A number decreased by 6.

n - 6

Example 3: The product of 16 and a.

16a

Example 4: The difference of 7 and 4 times a number x.7 – 4xExample 5: Twice the sum of 15 and a number

2(15 + n)

Write a Verbal Expression Write a Verbal Expression for each Example.for each Example.

Example 6: c2 + 21d

Example 7 : 4n5

7

C squared increased by the C squared increased by the product of 21 and d.product of 21 and d.

4 multiplied by n to the fifth 4 multiplied by n to the fifth power divided by 7.power divided by 7.

Find the UNIT RATEFind the UNIT RATE

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Section 1.4: Write Equations and Section 1.4: Write Equations and Inequalities. Inequalities.

SymbSymbolol

MeaningMeaning Associate WordsAssociate Words

== is equal tois equal to the same asthe same as

<< is less thanis less than fewer thanfewer than

<< is less than or is less than or equal toequal to

at most, no more thanat most, no more than

>> is greater is greater thanthan

more thanmore than

>> is greater is greater than or equal than or equal

toto

at least, no less thanat least, no less than

Write an equation or Write an equation or inequality.inequality.

1. The sum of twice a number r and 3 is 11.

2r + 3 = 11

2. The quotient of a number n and 2 is at most 16.

n2

< 16

Write an equation or Write an equation or inequality.inequality.

3. A number q is at least 5 and less than 17.

q<5 < 17

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Check whether the given number is Check whether the given number is a solution of the equation or a solution of the equation or

inequality.inequality.

1. 8 – 2x = 2; 3

8 – 2(3) = 2

8 – 6 = 2

2 = 2

Check whether the given number is Check whether the given number is a solution of the equation or a solution of the equation or

inequality.inequality.

2. 3 + 3p > 19; 5

3 + 3(5) > 193 + 15 > 19

18 > 19

MENTAL MATHMENTAL MATH:: Solve the Solve the equation using mental equation using mental

math!math!

1. x + 5 = 12- 5 - 5

x = 7

2. x - 6 = 3+ 6 + 6

x = 9

3. 8x = 328

x = 4

84. x = 4

77

x = 28

7

Section 1.6: Functions and Section 1.6: Functions and TablesTables

DomainDomain• The set of the first numbers of the ordered pairs.

RangeRange• The set of the second numbers of the ordered pairs.

Identify the domain and Identify the domain and range of the function.range of the function.

InputInput OutpuOutputt

00 00

11 22

44 88

66 1212

Domain:0, 1, 4, 6Range:0, 2, 8,

12

Domain:-2, 0, 2, 4Range:-8, 0, 8,

16

FUNCTIONS:FUNCTIONS:

The domain(x) are matched with only one range(y).

The “x’s” can not repeat themselves.

Is this a FUNCTION?Is this a FUNCTION?

InputInput OutpuOutputt

00 00

11 22

22 77

00 44

InputInput OutpuOutputt

-2-2 00

11 22

22 22

33 44

Make a table for the function.Make a table for the function.

Domain: 12, 15, 22, 30

InputInput

OutputOutput

InputInput 1212 1515 2222 3030

OutputOutput

InputInput 1212 1515 2222 3030

OutputOutput 99

InputInput 1212 1515 2222 3030

OutputOutput 99 1212

InputInput 1212 1515 2222 3030

OutputOutput 99 1212 1919

InputInput 1212 1515 2222 3030

OutputOutput 99 1212 1919 2727

Section 1.7: Functions as Section 1.7: Functions as GraphsGraphs

Coordinate Plane

y-axisThe vertical number line.

x-axisThe horizontal number line.

Origin(0, 0)

Plot each point on the coordinate plane.Plot each point on the coordinate plane.

E (5, 3)

F (-2, -1)

G (3.5, 4.5)

H (0, -6)

I (-5, 4)

E

F

G

H

I

Graph the function y = 2x - 3 Graph the function y = 2x - 3 with domain 2, 3, 5, 6. with domain 2, 3, 5, 6.

Step 1: Make an Input/Output Table.

InputInput

OutputOutput

2 3 5 6 1 3 7 9

Step 2: Plot the points.

Make an Input/Output Table.

InputInput

OutputOutput

1

2

3

4

5

6

7

8

Domain:1, 3, 5, 7Range:2, 4, 6, 8

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