algebra chapter 1. 1.1 – evaluating expressions evaluate the expression when c = 4. 1. 4c2. 83. 15...
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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
Please Excuse My Dear Aunt
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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.
Let’s Look at the Following Let’s Look at the Following SiteSite
https://www.classzone.com/books/https://www.classzone.com/books/algebra_1_2007_na/animations/algebra_1_2007_na/animations/explore_learning/chapter_1/explore_learning/chapter_1/dswmedia/1_3_Order_Ops.htmldswmedia/1_3_Order_Ops.html
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
hours
miles
2
110
hour
miles
1
55
gamesvideo5
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classes
students
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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
Let’s look at these Let’s look at these examplesexamples
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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
HOMEWORKHOMEWORK
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