How do you determine if #f(x)= x^4  4x^2# is an even or odd function?
a function is odd if
a function is even if
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To determine if a function (f(x) = x^4  4x^2) is even or odd, we can use the properties of even and odd functions.

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

Odd Function: A function (f(x)) is odd if (f(x) = f(x)) for all (x) in the domain of (f).
Let's check both conditions for (f(x) = x^4  4x^2):

Even Function: Substitute (x) into (f(x)): (f(x) = (x)^4  4(x)^2) Simplify: (f(x) = x^4  4x^2)
Since (f(x) = f(x)) for all (x), the function (f(x) = x^4  4x^2) is an even function.

Odd Function: Substitute (x) into (f(x)): (f(x) = (x)^4  4(x)^2) Simplify: (f(x) = x^4  4x^2)
Since (f(x) = f(x)) and not (f(x)) for all (x), the function (f(x) = x^4  4x^2) is not an odd function.
Therefore, (f(x) = x^4  4x^2) is an even function.
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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.
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