Do Now Find the following: (f + g)(-1) = (g ͦ f)(x) = (g - f)(2) = (f /g)(x) =

Slides:

Advertisements

Similar presentations

Combining Like Terms.

Advertisements

WARM UP Zeros: Domain: Range: Relative Maximum: Relative Minimum:

Symmetry of Functions Even, Odd, or Neither?. Even Functions All exponents are even. May contain a constant. f(x) = f(-x) Symmetric about the y-axis.

C ollege A lgebra Functions and Graphs (Chapter1) 1.

Even and Odd Functions madelinemontavon.cmswiki.wikispaces.net September 30th.

FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.

Lesson 3.1 Objective: SSBAT define and evaluate functions.

More on Functions and Their Graphs

WRITING EQUATIONS IN SLOPE INTERCEPT FORM 4.2. What you need… ■In order to write an equation in slope intercept form you need to know 2 things: ■ y =

Equal distance from origin.

Section 2.4 Symmetry Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

Warm Up Find the following: (f + g)(-1) = (g f)(x) = (g - f)(2) = (f /g)(x) =

FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.

AIM: What is symmetry? What are even and odd functions? Do Now : Find the x and y intercepts 1)y = x² + 3x 2) x = y² - 4 (3x + 1)² HW #3 – page 9 (#11-17,

Warm-Up. FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.

Section 3.1 Power Functions.

Definition: Even Function

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

More on Functions and Their Graphs

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Or ODD EVEN Functions.

Symmetry Section 2.7 Notes (part 2).

Warm up Find f(-3). 4 Find g(0).

Properties Of Functions 1.3

Core Focus on Functions & Data

Equation Invasion Objective: I can solve two-step equations using the opposite operation to determine the value of an unknown variable.

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

Evaluate and Graph Polynomial Functions

Algebra Algebra.

3.1 Lesson Only! Skill Check

Exponential Functions are functions which can be represented by graphs similar to the graph on the right.

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

Points of Intersection

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

Bellwork Find the x and y values Y (-5,2) (3,3) X (-3,-1) (4,-3)

Warm up Find f(-3). 4 Find g(0).

Section 2.4 Symmetry.

Warm up Find f(-3). 4 Find g(0).

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

Expressions and Equations

Properties of Functions

Introduction to Functions

Properties of Functions

Section 2.4 Symmetry Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

Skills Check Find f(-3). 4 Find g(0).

Functions: Even/Odd/Neither

Power Functions Investigating symmetry to determine if a power function is even, odd, or neither.

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

Chapter 2 More on Functions.

Properties of Functions

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

Warm up Factor..

Warm up Find f(-3). 4 Find g(0).

REFLECTIONS AND SYMMETRY

Part 5: Even and Odd Functions

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

Properties of Functions

Properties of Functions

Properties of Functions

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

Section MATH 1310 Section 3.2

Presentation transcript:

Do Now Find the following: (f + g)(-1) = (g ͦ f)(x) = (g - f)(2) = (f /g)(x) =

Even & Odd Functions

What are even & odd functions? Plug in 3 to this equation… Now plug in -3… What do you notice about the answers?

What are even & odd functions? Plug in 3 to this equation… Now plug in -3… What do you notice about the answers?

What are even & odd functions? Plug in 3 to this equation… Now plug in -3… What do you notice about the answers?

Even Functions A function is even when it is symmetric about the y-axis. Meaning when you plug in –x the function simplifies to be the same f(-x) = f(x) Examples:

Odd Functions A function is odd when it is symmetric about the origin - the point (0,0) Meaning when you plug in –x & simplify the signs of each term changes! f(-x) = - f(x) Examples:

Functions that are NEITHER A function is neither when it is NOT symmetric about the y-axis or the origin Most functions are neither even nor odd Meaning when you plug in –x you get a completely different function that is not the same & does not have all signs changed Examples:

So Basically… Plug in a negative and get Same # Different Signs  Odd Plug in a negative and get a Same Number Same Sign  Even

Even Functions-Graphing

Even Functions Graphing Determine which are even…

Odd Functions-Graphing

Odd Functions Graphing Determine which are odd…

Even Functions-Algebraically Plug in –x and simplify! If you get the same function, it is even! Note: If the function has all EVEN exponents and/or a constant (#) it will be even! That means it has variable exponents of 2,4,6,etc…

Odd Functions-Algebraically Plug in –x and simplify! If you get the opposite function, it is odd! Note: If the function has all ODD exponents & NO constant it will be odd! That means EVERY variable term has an exponent of 1,3,5,7,etc…

Neither Functions-Algebraically Plug in –x and simplify! If you do not get the same function, or all of the signs do not change, it is neither! Still -5 If the function has a mixture of even or odd exponents, or odd exponents & a constant then it will be neither! This is the MOST COMMON!

Example:

Example:

Example:

Example:

Example:

Example: Determine if the function is even, odd, or neither.

Example: Determine if the function is even, odd, or neither.

Example: Determine if the function is even, odd, or neither.

Example: Determine if the function is even, odd, or neither.

Example: Determine if the function is even, odd, or neither.

Example: Determine if the function is even, odd, or neither.

Example: Determine if the function is even, odd, or neither.

Example: Determine if the function is even, odd, or neither.

NC Final Exam Question Example Which of the following is an even function?

Challenge Question Is (x+1)2 even, odd, or neither?

Challenge Question Can a function be both even and odd?

Homework Worksheet front and back! Don’t forget to Justify!!! Graphs & multiple choice questions from http://www.mathsisfun.com/algebra/functions-odd-even.html