How do you determine if #f(x)=(6x )/( x^2 + 6)# is an even or odd function?
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To determine if a function is even or odd, we evaluate whether it satisfies the conditions of evenness or oddness:
 Even function: f(x) = f(x) for all x in the function's domain.
 Odd function: f(x) = f(x) for all x in the function's domain.
For the function f(x) = (6x)/(x^2 + 6):

To check for evenness, substitute x for x and see if the function remains the same. f(x) = (6(x))/((x)^2 + 6) f(x) = (6x)/(x^2 + 6)

To check for oddness, substitute x for x and see if the function becomes the negative of the original function. f(x) = (6(x))/((x)^2 + 6) f(x) = (6x)/(x^2 + 6)
Comparing the results:
 Since f(x) = f(x), the function is odd.
Therefore, f(x) = (6x)/(x^2 + 6) is an odd 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.
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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