Question

Dimetri says that a function that is made of terms where the variables is raised only to an odd power will be an odd function.Do you agree with dimetri? Explain Why or Why not.

Answer 1

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 product is positive.

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 odd exponent of a negative number, the outcome is negative.

Then for functions with only odd exponents, the outcome for evaluating the function in a given input is exactly the opposite of evaluating the same function with the opposite input.

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