Discovering The Oddness Of A Function: Rules And Examples

Is the function odd, even, or neither: {(0,0), (1,1)(-1, -1), (2, 2) (-2, -2)}

ODD

To determine whether the function is odd, even or neither, we need to use the rules:

– A function is even if f(-x) = f(x) for all x in the domain of the function
– A function is odd if f(-x) = -f(x) for all x in the domain of the function
– A function is neither even nor odd if it does not satisfy the above conditions

Let’s check if the function is even:

f(-x) = f(x) for all x in the domain of the function

f(-1) = -1, f(1) = 1, f(-2) = -2, f(2) = 2

Since the function values are not equal to each other for the opposite inputs, the function is not even.

Now let’s check if the function is odd:

f(-x) = -f(x) for all x in the domain of the function

f(-1) = -1, f(1) = 1, f(-2) = -2, f(2) = 2

Since the function values are equal in magnitude but opposite in sign for the opposite inputs, the function is odd.

Therefore, the function is odd.

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