1.4%20Absolute%20Values

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1.4 Absolute Values

• Solving Absolute Value Equations
• By putting into one of 3 categories

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What is the definition of Absolute Value?

• __________________________________
• __________________________________
• Mathematically,
• ___________________
• For example, in , where could x be?
  

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-3
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• To solve these situations, _______________________
  __________________________________________________
  _____________________________
• Consider
• ________________________

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That was Category 1

• Category 1 ____________________________
• _______________________________________
• _______________________________________

Example Case 1 Case 2
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Absolute Value Inequalities

• Think logically about another situation.
• What does mean?
• For instance, in the equation ,
• _________________________________

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• How does that translate into a sentence?
• __________________________________
• Now solve for x.
• This is Category 2 when x is less than a number

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Absolute Value Inequalities

• What does mean?
• In the equation ,
• __________________________________

0
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Less than And statement
Greater than Or statement
Note ? is the same as ? ?is the same as ? just
have the sign in the rewritten equation match the
original.
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Isolate Absolute Value

• _______________________________________
• ______________________________________
• ______________________________________

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When x is on both sides

• ______________________________________
• ________________________________________
• ______________________________________

Case 1 Case 2
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Example inequality with x on other side
Case 1 Case 2
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Examples
Case 1 Case 2
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Case 1 Case 2
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Case 1 Case 2
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_________________________________
Whats wrong with this? __________________________
__________________________________________________
________
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1-4 Compound Absolute ValuesEqualities and
Inequalities

• More than one absolute value in the equation

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Some Vocab

• Domain- _________________________
• Range- __________________________
• Restriction- _______________________
• __________________________________________________
  ________________

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Find a number that works.
We will find a more methodical approach to find
all the solutions.
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In your approach, think about the values of this
particular mathematical statement in the 3
different areas on a number line.

• -_________________________________________
• ________________________________________
• - ________________________________________

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It now forms 3 different areas or cases on the
number line.

• ______________________________
• ______________________________
• ___________________________________

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Case 1 Domain
________________________
__________________________________________________
__
__________________________________________________
_________________________________________________
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Case 2 Domain
___________________________________
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Case 3 Domain
_____________________________
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• Final Answers
• ______________________________
• ______________________________
• _____________________________

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-2
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If you get an answer in any of the cases where
the variable disappears and the answer is TRUE
________________________________ ________________
__________________________________________________
______________________________
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1-5 Exponential Rules
You know these already
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Review of the Basics
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Practice problems
Simplify each expression
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Do NOT use calculators on the homework, please!!
?
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RuleIf bases the same set exponents equal to
each other
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1-6 Radicals (Day 1) and Rational Exponents (Day
2)
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What is a Radical?

• In simplest term, it is a square root ( )
• ________________

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• The Principle nth root of a
• 1.
• If a lt 0 and n is odd then is a negative
  number ___________________
• If a lt 0 and n is even, _____________ __________
  

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Vocab
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Lets Recall
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Rules of Radicals

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Practice problems
Simplify each expression
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Class Work problems
Simplify each expression
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1-6 Radicals (Day 1) and Rational Exponents (Day
2)
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What is a Rational Exponent?

• ____________________________________
• ____________________________________
• ____________________________________
• ____________________________________

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Dont be overwhelmed by fractions!

• These problems are not hard, as long as you
  remember what each letter means. Notice I used
  p as the numerator and r as the denominator.
  
• p _____________________________
• r _____________________________
• ________________________________________
• ________________________________________
• ________________________________________

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Practice problems
Simplify each expression
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The last part of this topic

• What is wrong with this number?
• ___________________________________
• ___________________________________
• ___________________________________

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Rationalizing

• If you see a single radical in the denominator
  ______________________________________
• ________________________________________
• ________________________________________
• ________________________________________

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Rationalizing

• If you see 1 or more radicals in a binomial, what
  can we do?

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What is a Conjugate?

• The conjugate of a b ______. Why?
• The conjugate _______________________
• ___________________________________
• ___________________________________
• ___________________________________

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Rationalizing

• Multiply top and bottom by the conjugate! Its
  MAGIC!!

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1.7 Fundamental Operations
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Terms

• Monomial ______________________________
• Binomial _______________________________
• Trinomial ______________________________

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• Standard form
• _______________________________________
• Collecting Like terms

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• F ____________
• O ____________
• I ____________
• L ____________

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• Examples

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1-8 Factoring Patterns
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What is the first step??

• _____

Why? __________________________________ __________
________________________ ________________________
__________ ___________________________________
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Perfect Square Trinomial
Factors as
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Difference of squares
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Sum/Difference of cubes
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3 terms but not a pattern?

• This is where you use combinations of the first
  term with combinations of the third term that
  collect to be the middle term.

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4 or more terms?

• ________________________________________
• ________________________________________
• ________________________________________
• ________________________________________
• ________________________________________
• ________________________________________
• ________________________________________

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Examples
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Solve using difference of Squares
Solve using sum of cubes
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Examples of Grouping
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Examples of Grouping
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1.9 Fundamental Operations

• What are the Fundamental Operations?

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Addition, Subtraction, Multiplication and Division

• We will be applying these fundamental operations
  to rational expressions.
• This will all be review. We are working on the
  little things here.

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Simplify the following

• Hint __________________________________
• _______________________________________
• _______________________________________

1. What is the domain of problem 1?

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_______________________________ _________________
______________ Lets Watch.
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Polynomial Long Division
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Polynomial Long Division
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1-10 Introduction to Complex Numbers

• What is a complex number?

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To see a complex number we have to first see
where it shows up

• Solve both of these

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Um, no solution????

• does not have a real
  answer.
• It has an imaginary answer.
• To define a complex number ____________
• ___________________________________
• This new variable is i

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• Definition
• Note __________________
• So, following this definition
• ______________________________
• ______________________________
• ______________________________
• ______________________________

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And it cycles.
Do you see a pattern yet?
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What is that pattern?

• We are looking at the remainder when the power is
  divided by 4.
• Why?
• ___________________________________
• ___________________________________
• ___________________________________
• Try it with

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Hints to deal with i

• 1. __________________________________
• 2. __________________________________
• ____________________________________
• _________________________________
• ____________________________________

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Examples
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OK, so what is a complex number?

• ______________________________
• ______________________________
• A complex number comes in the form
• a bi

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Lets try these 4 problems.
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