How do you determine if #x^2 - 4# is an even or odd function?
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To determine if ( x^2 - 4 ) is an even or odd function, we examine its symmetry properties:
- Even Function: If ( f(x) = f(-x) ) for all ( x ) in the domain of the function, then the function is even.
- Odd Function: If ( f(x) = -f(-x) ) for all ( x ) in the domain of the function, then the function is odd.
For ( f(x) = x^2 - 4 ):
- ( f(-x) = (-x)^2 - 4 = x^2 - 4 = f(x) )
The function ( f(x) = x^2 - 4 ) satisfies the condition for an even function because ( f(x) = f(-x) ) for all ( x ) in its domain. Therefore, ( x^2 - 4 ) is an even function.
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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.
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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