Chapter 8 Irrational Roots Clark/Anfinson. CHAPTER 8 – SECTION 1 Root functions.

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Presentation transcript:

Chapter 8 Irrational Roots Clark/Anfinson

CHAPTER 8 – SECTION 1 Root functions

Investigating a function

Graph

What the graphs tell us Even roots domain is restricted Range is restricted generally increasing Negatives cause decreasing behavior Not a constant rate of increase or decrease Odd root Domain is not restricted Range is not restricted generally increasing Negatives cause decreasing behavior Not a constant rate of increase or decrease

Finding domain and range

Domain and range continued

Answering f(x) questions using graph Use the graph to find f(4), f(6) and f(-3) Use the graph to find where f(x) = 2, f(x) = 3.5

CHAPTER 8 - SECTION 2 Simplify/add-subtract irrational roots

Irrational numbers

Simplifying radicals A radical is considered simplified when there are no factors within the radical that are higher powers than the root. ie. If the root is 2 there are NO powers inside the radical if the root is 3 there are no square powers inside the radical

Addition and radicals

Examples

Simplify radicals BEFORE you add

CHAPTER 8 – SECTION 3 Multiplying/dividing radicals

2 variations on rule

Examples

Multiplication with addition

Division with radicals

CHAPTER 8 – SECTION 4 Solving radical equations

Solving – isolate the variable by inversing You can do ANYTHING to an equation as long as you change both SIDES the same way. Anything includes inserting and exponent on the WHOLE side

Example

How restrictions affect solving

CHAPTER 8 – SECTION 5 Imaginary numbers

Definition

Examples

Simplifying Complex numbers