- 56

- 0

## Main Question or Discussion Point

Can someone prove even and odd fucntions for me not through examples but by actually proving them?

Thanks

Thanks

- Thread starter darthxepher
- Start date

- 56

- 0

Can someone prove even and odd fucntions for me not through examples but by actually proving them?

Thanks

Thanks

- 623

- 0

Well how do you define even and how do you define odd functions?

- 56

- 0

A function f is odd if the graph of f is symmetric with respect to the origin. Algebraically, f is odd if and only if f(-x) = -f(x) for all x in the domain of f

I need an algebraic proof using angles and algebra... its for my trig class.

- 623

- 0

- 56

- 0

Is that a proof though?

- 623

- 0

Yes... you are taking a definition and using it. What's a proof in your opinion?

- 726

- 1

You are **defining** even and odd functions to have those properties. There is no need for a proof.

- 56

- 0

IS there a way to prove an even and odd function?

- 726

- 1

symbolipoint

Homework Helper

Education Advisor

Gold Member

- 5,730

- 979

Start with a specific function and test it for identity of evenness and oddness according to the definition for even and odd functions.Can someone prove even and odd fucntions for me not through examples but by actually proving them?

Thanks

- 623

- 0

- 56

- 0

so could an axiom be f(x)=|x|?

- 623

- 0

symbolipoint

Homework Helper

Education Advisor

Gold Member

- 5,730

- 979

USE the Definitions of EVEN functions and ODD functions. Does one statement or the other become an identity?so could an axiom be f(x)=|x|?

Check:

|-x|=|x|

Check:

|-x|=-|x|

It one of those or both of those or neither of those true? What is the meaning?

Mentallic

Homework Helper

- 3,797

- 94

HallsofIvy

Science Advisor

Homework Helper

- 41,738

- 897

The reflection of (x,y) in the y-axis is the point (-x, y). If f is an even function and y= f(x), what are (x, y) and (-x, y) in terms of the graph of f? Are they both on the graph?

The point "symmetric" to (x, y) in the origin is (-x, -y). If f is an odd function and y= f(x), what are (x, y) and (-x, -y) in terms of the graph of f? Are they both on the graph?

- Last Post

- Replies
- 3

- Views
- 5K

- Last Post

- Replies
- 3

- Views
- 2K

- Last Post

- Replies
- 2

- Views
- 2K

- Last Post

- Replies
- 3

- Views
- 2K

- Last Post

- Replies
- 9

- Views
- 7K

- Last Post

- Replies
- 5

- Views
- 2K

- Last Post

- Replies
- 10

- Views
- 3K

- Last Post

- Replies
- 28

- Views
- 804