Here we want to study the relation between the exponents in a polynomial function and the "odd" property of functions.
We will see that Dimetri is correct.
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We start by defining an odd function as a function such that:
f(-x) = -f(x).
Now, let's see a simple function with only odd exponents.
f(x) = a*x (the exponent is 1, so it is odd).
if we evaluate this in x = 1, we get:
f(1) = a
If we evaluate this in x = -1, we get:
f(-1) = a*-1 = -a
Then this is odd.
Now let's see a more general case and why Dimetri is correct.
For the rule of signs, when we multiply 2 negative numbers, the <u>product is positive.</u>
So always that we have an even exponent on a negative number, the outcome will be positive.
This does not happen for odd exponents, because we can't separate all the products in groups of 2, thus if we take the <u>odd exponent of a negative number, the outcome is negative</u>.
Then for functions with only odd exponents, the <u>outcome for evaluating the function in a given input is exactly the opposite of evaluating the same function with the opposite input</u>.
This means that the function is odd.
Again, note that this only happens if the function only has odd exponents.
If you want to learn more, you can read:
brainly.com/question/15775372
