Are these functions odd, even or neither, and can you explain why: y=x^3 and y=3/1+x^2?

Answer 1

Look at the greatest exponent of x. If it is odd, it is an function. If it is even, then it is an even function.

Test: Substitute (-x) into f(x).

If f(-x) = f(x), then function is even.

If f(-x) = -f(x), then it is odd.

If f(-x) not = f(x), then neither.

Answer 2

for an even function, this rule applies:
f(x)=f(-x)
in other words, no matter whether your x value is positive or negative, your y value is NOT going to change.
ex: y=x^2 + (3/1, or 1/3, or whatever number). both +3 and -3 result in a positive number, so this is even.

in an odd function,
f(-x)= -f(x)
in other works, making your x value negative is the same as making your y value negative (a negative input will result in a negative output)
f(x)=x^3 must be odd.
f(2)=2^3 = 8
f(-2)= -2^3 = -8
-f(2)=2^3 =8, f(2) = -8
f(-2)= -f(2), so it's odd :)

*when looking at a graph, an odd function is symmetrical ABOUT THE ORIGIN.

Answer 3

f(-x)=(-x)^3=-x^3=-f(x),so function is odd.
& f(-x)=3/1+(-x)^2=3/1+x^2=f(x),so function is even.
If f(-x) is neither of the above,it is none.

Answer 4

y = f(x) = x^3
f(-x) = -x^3 = - f(x) so function is odd

y=3/(1+ x^2)
f(-x) = 3/(1+(-x)^2) = 3/(1+x^2) = f(x) so it is even

Answer 5

when f(-x) = -f(x) the fn is odd
and f(-x) = f(x) the fn is even

So y = X^3 is odd and y=3/1 + x62 is even