# How do you determine if #f(x) = 3x^5 - 4x + 3# is an even or odd function?

So neither condition is satisfied.

For polynomial functions:

- If all of the terms are of odd degree then the function is odd.
- If all of the terms are of even degree then the function is even.
- If some of the terms are of odd degree and some even then the function is neither odd nor even.

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To determine if ( f(x) = 3x^5 - 4x + 3 ) is an even or odd function:

- For even functions, check if ( f(-x) = f(x) ) for all ( x ).
- For odd functions, check if ( f(-x) = -f(x) ) for all ( x ).

Substitute ( -x ) into ( f(x) ) and simplify: [ f(-x) = 3(-x)^5 - 4(-x) + 3 ] [ = -3x^5 + 4x + 3 ]

Now compare ( f(-x) ) with ( f(x) ): [ f(-x) = -3x^5 + 4x + 3 ] [ f(x) = 3x^5 - 4x + 3 ]

Since ( f(-x) ) is not equal to ( f(x) ) and also not equal to the negative of ( f(x) ), the function ( f(x) = 3x^5 - 4x + 3 ) is neither even nor 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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