'Odd functions' diaporamas de présentation

Periodic Functions and Fourier Series

Periodic Functions and Fourier Series. A function. is periodic. if it is defined for all real . such that. Periodic Functions. and if there is some positive number,. . be a periodic function with period. Fourier Series. The function can be represented by a trigonometric series as:.

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Welcome Back!

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College Algebra

College Algebra. Acosta/ Karwowski. Non-linear functions. Unit 2 -a. Nonlinear functions. Chapter 3. Analyzing functions. Analyzing a function means to learn all you can about the function using tables, graphs, logic, and intuition

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1.5 Logarithms

1.5 Logarithms. In other words, a function is one-to-one on domain D if: . whenever. A relation is a function if: for each x there is one and only one y . A relation is a one-to-one if also: for each y there is one and only one x . .

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Discrete-Time Signal Description

Discrete-Time Signal Description. Sampling and Discrete Time. Sampling and Discrete Time. Sinusoids. Sinusoids. Periodic. Periodic. Periodic. Aperiodic. Sinusoids. An Aperiodic Sinusoid. Sinusoids. Sinusoids. Sinusoids. Exponentials. The Unit Impulse Function.

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TRIGONOMETRY

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5.1 Using Fundamental Identities

5.1 Using Fundamental Identities. Fundamental Trigonometric Identities. Fundamental Trigonometric Identities. Co functions. Even or Odd functions. Simplify the Trigonometric Identity . Given: . Simplify the Trigonometric Identity . Given: . Simplify the Trigonometric Identity . Given: .

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Even and Odd Functions

Even and Odd Functions. Algebraically. A function is even if. All of the exponents of the variable are even. A function is odd if. All of the exponents of the variable are odd. A function is neither if. The exponents are a mixture of odd and even. BEWARE OF CONSTANTS.

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More on Functions & Graphs 2.2

More on Functions & Graphs 2.2. JMerrill, 2007 Contributions by DDillon Revised 2008. Review. Find: Domain [-1, 4) Range [-5, 4] f(-1) f(-1) = -5 f(2) f(2) = 4. Difference Quotient. One of the basic definitions in calculus uses the difference quotient ratio:

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Integration by Substitution

Integration by Substitution. Antidifferentiation of a Composite Function. Antidifferentiation of a Composite Function.

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Obtaining Information from Graphs

Obtaining Information from Graphs. You can obtain information about a function from its graph. At the right or left of a graph, you will find closed dots, open dots, or arrows. A closed dot indicates that the graph does not extend beyond this point and the point belongs to the graph.

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Reflections and Symmetry

Reflections and Symmetry. Lesson 5.2. Across the x-axis. Across the y-axis. Flipping the Graph of a Function. Given the function below We wish to manipulate it by reflecting it across one of the axes. Flipping the Graph of a Function. Consider the function

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Reflections and Symmetry

Reflections and Symmetry. Lesson 5.2. Across the x-axis. Across the y-axis. Flipping the Graph of a Function. Given the function below We wish to manipulate it by reflecting it across one of the axes. Flipping the Graph of a Function. Consider the function

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PRECALCULUS I

PRECALCULUS I. Functions and Graphs Function, domain, independent variable Graph, increasing/decreasing, even/odd. Dr. Claude S. Moore Danville Community College. Definition: Function.

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5.5 The Substitution Rule

5.5 The Substitution Rule. The Substitution Rule. If u=g(x) is differentiable function whose range is an interval I , and f is continuous on I , then The Substitution rule is proved using the Chain Rule for differentiation.

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Lesson 3.1 Graph Cubic Functions

Lesson 3.1 Graph Cubic Functions. Goal Graph and analyze cubic functions. Vocabulary Page 126. A cubic function is a nonlinear function that can be written in the standard form y = ax 3 + bx 2 + cx + d where a ? 0. A function f is an odd function if f (- x ) =- f ( x ).

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Symmetry and Coordinate Graphs Section 3-1

Symmetry and Coordinate Graphs Section 3-1. How do we determine symmetry using algebra? How do we classify functions as even or odd?. Essential Questions:. Possible types of symmetry are:. with respect to the x -axis with respect to the y -axis with respect to the origin

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Symmetry, Even and Odd Functions

Symmetry, Even and Odd Functions. Notes: 9/11. Symmetry, even and odd functions. A graph is symmetric i f it can be reflected over a line and remain unchanged. y = x 2 i s symmetric over the y-axis. The y-axis is called the axis of symmetry. Symmetry, even and odd functions.

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Trig Functions of Real Numbers

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Do Now

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