How do you determine if #g(x)= 9x^3  8# is an even or odd function?
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To determine if the function ( g(x) = 9x^3  8 ) is even or odd, follow these steps:

Even Function: A function ( f(x) ) is even if ( f(x) = f(x) ) for all ( x ) in the domain.

Odd Function: A function ( f(x) ) is odd if ( f(x) = f(x) ) for all ( x ) in the domain.
For ( g(x) = 9x^3  8 ):

Substitute ( x ) into the function: ( g(x) = 9(x)^3  8 ).

Simplify ( g(x) ): ( g(x) = 9(x)^3  8 = 9(x^3)  8 = 9(x^3)  8 ).
Now, compare ( g(x) ) with ( g(x) ):

If ( g(x) = g(x) ), then the function is even.

If ( g(x) = g(x) ), then the function is odd.
For ( g(x) = 9x^3  8 ), ( g(x) ) does not equal ( g(x) ) and ( g(x) ) does not equal (g(x)), so ( g(x) ) is neither even nor odd.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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