# How do you determine if #f(x) = x - absx# is an even or odd function?

An even function is a function where

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To determine if ( f(x) = x - |x| ) is an even or odd function:

- Even function: ( f(x) = f(-x) ) for all ( x ) in the domain.
- Odd function: ( f(x) = -f(-x) ) for all ( x ) in the domain.

For the given function:

( f(x) = x - |x| )

Replace ( x ) with ( -x ):

( f(-x) = -x - |-x| )

Simplify:

( f(-x) = -x - |x| )

Compare ( f(-x) ) with ( f(x) ):

( f(-x) = -f(x) )

Since ( f(-x) = -f(x) ), the function is odd.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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