How do you determine if #f(x)= x^3 + 1# is an even or odd function?
neither
Examine the following to see if a function is even or odd.
• f(x) is even if f(x) = f( x)
There is symmetry in functions about the yaxis.
• f(x) is odd if f(x) =  f(x).
There is symmetry around the origin of odd functions.
Check for even
f(x) is not even since f(x) ≠ f(x).
Check for odd
f(x) is not odd since f(x) ≠  f(x).
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To determine if a function is even or odd, we need to examine its symmetry.
 Even functions have symmetry about the yaxis, meaning that f(x) = f(x) for all x in the domain.
 Odd functions have rotational symmetry of 180 degrees about the origin, meaning that f(x) = f(x) for all x in the domain.
For the function f(x) = x^3 + 1:

Check for even symmetry: f(x) = x^3 + 1 f(x) = (x)^3 + 1 = x^3 + 1 Since f(x) is not equal to f(x), the function is not even.

Check for odd symmetry: f(x) = x^3 + 1 f(x) = (x)^3  1 = x^3  1 Since f(x) is not equal to f(x), the function is not odd.
Therefore, the function f(x) = x^3 + 1 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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