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- Chapter 1 Linear Functions
- Chapter 2 Quadratic Functions
- Chapter 3 Quadratic Equations and Complex Numbers
- Chapter 4 Polynomial Functions
- Chapter 5 Rational Exponents and Radical Functions
- Chapter 6 Exponential and Logarithmic Functions
- Chapter 7 Rational Functions
- Chapter 8 Sequences and Series
- Chapter 9 Trigonometric Ratios and Functions
- Chapter 10 Probability
- 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.
emathinstruction
Jan 3, 2017
In this lesson we learn what makes some functions even and what makes some functions odd.
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Solutions for BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015 1st
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Common Core Algebra 2 Math (Worksheets, Homework, Lesson Plans)
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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) |
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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) |
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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, 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.
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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.
Find step-by-step solutions and answers to Algebra 2 Common Core - 9780133186024, as well as thousands of textbooks so you can move forward with confidence. ... Algebra 2 Common Core. 1st Edition. Basia Hall, Charles, Kennedy. ISBN: 9780133186024. Alternate ISBNs. ... Chapter 2:Functions, Equations, and Graphs. Page 57: Get Ready! Section 2-1 ...
By this, you can finish your homework problems in time. By practicing the problems from our answer key students can prove their best in all types of exams like practice tests, FAs, Quiz, Chapter tests, and so on. Have a look at the list of the chapters given below and start practicing the problems. Chapter 1 Linear Functions.
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 ...
Selected Answers Topic 1 PearsonRealize.com 14. The student reflected the graph of f(x) across the x-axis instead of reflecting the graph across the y-axis. y 4 2 O x ˜2 ˜4 ˜4 ˜2 2 4 f g 16. g(x) = f (−x) = (−x) 2 = (x) 2 The graph of g(x) is the same as the graph of f (x). 18. y 4 2 O x ˜2 ˜4 ˜ ˜2 24 f g The domain values of f and ...
iz. .com Selected AnswersLesson 1-11. The domain and range of a function give information about all the possible inpu. s and outputs for the relationship. The x- and y-intercepts of the function's graph give information about what happens to the relations. ip when one of the quantities is 0. The graph also shows whether the quantities in the ...
Algebra 2 Lessons and Practice is a free site for students (and teachers) studying a second year of high school algebra. Practice with Odd/Even Functions MathBitsNotebook.com Topical Outline | Algebra 2 Outline | MathBits ... Show your algebraic work to confirm your answers. 1) f (x) = 4x 3 - 9: 2) f (x) = x 2 + 4x + 4: 3) f (x) = x 5 + 4x 3 ...
Common Core Algebra II; Algebra 2 + Trigonometry; Standards Alignment; Shop. N-Gen Math™ 6; N-Gen Math™ 7; ... Even and Odd Functions. LESSON/HOMEWORK. LESSON VIDEO. ANSWER KEY. EDITABLE LESSON. EDITABLE KEY. ... We ask that you help us in our mission by reading and following these rules and those in our Single User License Agreement.
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...
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In this lesson we learn what makes some functions even and what makes some functions odd. Watch Common Core Algebra II.Unit 7.Lesson 5.Even and Odd Functions, Math, Middle School, Math, Algebra Videos on TeacherTube.
• 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
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 ...
2 f x x f f (b) 3 2 2 3 g x x g g (c) 5 41 14 h x x h h 2. Using STORE on your calculator, evaluate each of the following more complex functions. (a) gx 352 4 10 5 0 x fx x f f (b) 25 2 4 3 x x g g (c) x 30 1.2 3 0 hx h h 3. Based on the graph of the function y g x shown below, answer the following questions. (a) Evaluate g g g g 2 , 0 , 3 and 7 .
Step-by-step video answers explanations by expert educators for all BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015 1st by Ron Larson, Laurie Boswell only on Numerade.com ... Rational Exponents and Radical Functions. 6 sections 407 questions ... science,etc .It provide more accurate answer and it give all the answers even no one ...
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
Algebra 2 answers, solutions, and theory for high school math, 10th to 11th grade. Like a math tutor, better than a math calculator or problem solver. ... Pearson Algebra 2 Common Core, 2011. ISBN: 9780133186024. undefined Textbooks Browse chapters. Pearson Algebra 2 Common Core, 2013. ISBN: 9780133281163.
Find step-by-step solutions and answers to Algebra 2 Common Core Edition - 9780076639908, as well as thousands of textbooks so you can move forward with confidence. ... Section 6-2: Inverse Functions and Relations. Section 6-3: Square Root Functions and Inequalities. Section 6-4: nth Roots. Page 414: Mid-Chapter Quiz. Section 6-5: Operations ...
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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):