Math Gr.12 Polynomial Odd degree function?

Question

y= f(x)
put x= -x
when y = f(-x) = -f(x)
f(x) = x^3
f(-x) = (-x)^3
f(-x) = -x^3
f(-x) = -f(x)

then it is odd degree function...

WTF
I understand even degree function just when i was about to add it to this question but i dont understand odd degree functions..
please help?

Answer 1

If you click on 'wickipedia' there are volumes of analysis and descriptions regarding odd and even functions. Here is a taster:



Basic Properties:



The only function which is both even and odd is the constant function which is equal to zero (i.e., f(x) = 0 for all x).

The sum of an even and odd function is neither even nor odd, unless one of the functions is equal to zero over the given domain.

The sum of two even functions is even, and any constant multiple of an even function is even.

The sum of two odd functions is odd, and any constant multiple of an odd function is odd.

The product of two even functions is an even function.

The product of two odd functions is an even function.

The product of an even function and an odd function is an odd function.

The quotient of two even functions is an even function.

The quotient of two odd functions is an even function.

The quotient of an even function and an odd function is an odd function.

The derivative of an even function is odd.

The derivative of an odd function is even.

The composition of two even functions is even, and the composition of two odd functions is odd.

The composition of an even function and an odd function is even.

The composition of any function with an even function is even (but not vice versa).

The integral of an odd function from −A to +A is zero (where A is finite, and the function has no vertical asymptotes between −A and A).

The integral of an even function from −A to +A is twice the integral from 0 to +A (where A is finite, and the function has no vertical asymptotes between −A and A).



Hope it helps, Luvan!



:)>

Answer 2

Odd Degree Polynomial

Answer 3

If your Expression it's: F(x) = (x^4 - 6) / x^6 then F(x) it's a rational function not a polynomial. Rational functions hasn't degree.

Answer 4

"Odd degree" polynomial just means the largest exponent in the expanded polynomial is an odd integer. (Of course, the coefficient on this term must also be non-zero.)



Examples of odd degree polynomials:



f(x) = 3x

f(x) = -2x³ + 7x² - 9x + 3

f(x) = x^5



The degrees for these polynomials are 1, 3, and 5, all odd numbers.