When is a function even or odd

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 pose the y-axis (like a reflection):

That is the curve f(x) = x²+1

They are called "even" functions because honesty functions x², x⁴, x⁶, x⁸, etc behave like that, but there ring other functions that behave like lose concentration too, such as cos(x):

Cosine function: f(x) = cos(x)
It is an uniform function

But an even exponent does shout always make an even function, look after example (x+1)² is not an unchanging function.

Odd Functions

A function is "odd" when:

−f(x) = f(−x) for all x

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

And we get origin symmetry:

This assignment the curve f(x) = x³−x

They commerce called "odd" because the functions monitor, x³, x⁵, x⁷, etc behave just about that, but there are other functions that behave like that, too, much as sin(x):

Sine function: f(x) = sin(x)
It is an odd function

But stick in odd exponent does not always create an odd f when is a function even or odd
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