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  • Chapter 11 Data Analysis and Statistics

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Common Core Algebra II.Unit 7.Lesson 5.Even and Odd Functions

Middle school / math / algebra.

even and odd functions common core algebra 2 homework answers

emathinstruction

Jan 3, 2017

In this lesson we learn what makes some functions even and what makes some functions odd.

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Common Core Algebra 2 Math (Worksheets, Homework, Lesson Plans)

Related Topics: Common Core Math Resources, Lesson Plans & Worksheets for all grades

Looking for video lessons that will help you in your Common Core Algebra 2 math classwork or homework? Looking for Common Core Math Worksheets and Lesson Plans that will help you prepare lessons for Algebra 2 students?

The following lesson plans and worksheets are from the New York State Education Department Common Core-aligned educational resources. Eureka/EngageNY Math Algebra 2 Worksheets.

These Lesson Plans and Worksheets are divided into five modules.

Algebra 2 Homework, Lesson Plans and Worksheets

Topics and Objectives (Module 1)
Polynomial, Rational, and Radical Relationships





: Successive Differences in Polynomials ( )

: The Multiplication of Polynomials ( )

: The Division of Polynomials ( )

: Comparing Methods—Long Division, Again? ( )

: Putting It All Together ( )

: Dividing by 𝒙 − 𝒂 and by 𝒙 + 𝒂 ( )

: Mental Math ( )

: The Power of Algebra—Finding Primes ( )

: Radicals and Conjugates ( )

: The Power of Algebra—Finding Pythagorean Triples ( )

: The Special Role of Zero in Factoring ( )

Factoring—Its Use and Its Obstacles



: Overcoming Obstacles in Factoring ( )

: Mastering Factoring ( )

: Graphing Factored Polynomials ( )

: Structure in Graphs of Polynomial Functions ( )

: Modeling with Polynomials—An Introduction ( )

: Modeling with Polynomials—An Introduction ( )

: Overcoming a Second Obstacle in Factoring—What If There Is a Remainder? ( )

: The Remainder Theorem ( )

: Modeling Riverbeds with Polynomials ( )

: Modeling Riverbeds with Polynomials ( )

Solving and Applying Equations—Polynomial, Rational, and Radical



: Equivalent Rational Expressions ( )

: Comparing Rational Expressions ( )

: Multiplying and Dividing Rational Expressions ( )

: Adding and Subtracting Rational Expression ( )

: Solving Rational Equations: Solving Rational Equations ( )

: Word Problems Leading to Rational Equations ( )

: A Focus on Square Roots ( )

: Solving Radical Equations ( )

: Linear Systems in Three Variables ( )

: Systems of Equations ( )

: Graphing Systems of Equations ( )

: The Definition of a Parabola ( )

: Are All Parabolas Congruent? ( )

: Are All Parabolas Similar? ( )

A Surprise from Geometry—Complex Numbers Overcome All Obstacles



: Overcoming a Third Obstacle to Factoring—What If There Are No Real Number Solutions? ( )

: A Surprising Boost from Geometry ( )

: Complex Numbers as Solutions to Equations ( )

: Factoring Extended to the Complex Realm ( )

: Obstacles Resolved—A Surprising Result ( )

Topics and Objectives (Module 2)
The Story of Trigonometry and Its Contexts





: Ferris Wheels—Tracking the Height of a Passenger Car ( )

: The Height and Co-Height Functions of a Ferris Wheel ( )

: The Motion of the Moon, Sun, and Stars—Motivating Mathematics ( )

: From Circle-ometry to Trigonometry ( )

: Extending the Domain of Sine and Cosine to All Real Numbers

: Why Call It Tangent?

: Secant and the Co-Functions

: Graphing the Sine and Cosine Functions

: Awkward! Who Chose the Number 360, Anyway?

: Basic Trigonometric Identities from Graphs

Understanding Trigonometric Functions and Putting Them to Use



: Transforming the Graph of the Sine Function

: Ferris Wheels—Using Trigonometric Functions to Model Cyclical Behavior

: Tides, Sound Waves, and Stock Markets

: Graphing the Tangent Function

: What Is a Trigonometric Identity?

: Proving Trigonometric Identities

: Trigonometric Identity Proofs

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  • McGraw Hill Glencoe Algebra 2, 2012
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  • McGraw Hill Glencoe Algebra 2, 2017
  • Pearson Algebra 2 Common Core, 2011
  • Pearson Algebra 2 Common Core, 2013

Even and Odd Functions

They are special types of functions

Even Functions

A function is "even" when:

f(x) = f(−x) for all x

In other words there is symmetry about the y-axis (like a reflection):

They are called "even" functions because the functions x 2 , x 4 , x 6 , x 8 , etc behave like that, but there are other functions that behave like that too, such as cos(x):

But an even exponent does not always make an even function, for example (x+1) 2 is not an even function.

Odd Functions

A function is "odd" when:

−f(x) = f(−x) for all x

Note the minus in front of f(x): −f(x) .

And we get origin symmetry :

They are called "odd" because the functions x, x 3 , x 5 , x 7 , etc behave like that, but there are other functions that behave like that, too, such as sin(x) :

But an odd exponent does not always make an odd function, for example x 3 +1 is not an odd function.

Neither Odd nor Even

Don't be misled by the names "odd" and "even" ... they are just names ... and a function does not have to be even or odd.

In fact most functions are neither odd nor even. For example, just adding 1 to the curve above gets this:

It is not an odd function , and it is not an even function either. It is neither odd nor even

Even or Odd?

Example: is f(x) = x/(x 2 −1) even or odd or neither.

Let's see what happens when we substitute −x :

So f(−x) = −f(x) , which makes it an Odd Function

Even and Odd

The only function that is even  and odd is f(x) = 0

Special Properties

  • The sum of two even functions is even
  • The sum of two odd functions is odd
  • The sum of an even and odd function is neither even nor odd (unless one function is zero).

Multiplying:

  • The product of two even functions is an even function.
  • The product of two odd functions is an even function.
  • The product of an even function and an odd function is an odd function.

IMAGES

  1. Even And Odd Functions Worksheet With Answers

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  2. Algebra 2 Homework-2 Odd Even Functions online exercise for

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  3. Common Core Algebra 2

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  4. graphs of even and odd functions worksheet answers

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  5. Common Core Algebra II.Unit 7.Lesson 5.Even and Odd Functions

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VIDEO

  1. The EXACT Steps to Solve This Algebra 2 Problem

  2. Common Core Algebra I.Unit #11.Lesson #5.Step Functions by eMathInstruction

  3. Common Core Algebra I.Unit #9.Lesson #5.Finding Zeroes by Completing the Square

  4. Even and odd functions: Problem type 2

  5. Even or Odd?

  6. Common Core.Algebra I.Unit #11.Lesson #3.Discrete Functions

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    Exercise #2: Consider the partial graph of the function f x shown twice below. Sketch the other half of the function if in (a) f x is even and in (b) f x is odd. The three coordinate pairs are listed to help you plot. y. (a) even (b) odd. y.

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    A function is neither even nor odd if it is not symmetric about the nor symmetric about the origin. y (x,y) (x,y) X Graphically determine whether the following functions are Even, Odd, or Neither symmetric Kiss about the origin Even symmetric 5 about the yaxis 0 Neither symmetric about the 10 nor about the origin Determine whether a function is ...

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  9. Even and Odd Functions: Common Core Algebra II

    Even f(x) = f(-x) its symmetric to the y axisOdd f(-x) = -f(x) symmetric to the originEven f(x) = f(-x) its symmetric to the y axisOdd f(-x) = -f(x) symmetri...

  10. Common Core Algebra II.Unit 7.Lesson 5.Even and Odd Functions

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    • Lesson #1 - Introduction to Functions • Lesson #2 - Function Notation • Lesson #3 - Function Composition • Lesson #4 - The Domain and Range of a Function • Lesson #5 - One to One Functions • Lesson #6 - Inverse Functions • Lesson #7 - Key Features of Functions

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    FREE Answers for BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015. Chapter. 1 Linear Functions 2 Quadratic Functions 3 Quadratic Equations And Complex Numbers 4 Polynomial Functions 5 Rational Exponents And Radical Functions 6 Exponential And Logarithmic Functions 7 Rational Functions 8 Sequence And Series 9 Trigonometric Rations And ...

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  20. Even and Odd Functions

    They are special types of functions. Even Functions. A function is "even" when: f(x) = f(−x) for all x In other words there is symmetry about the y-axis (like a reflection):. This is the curve f(x) = x 2 +1. They are called "even" functions because the functions x 2, x 4, x 6, x 8, etc behave like that, but there are other functions that behave like that too, such as cos(x):