Uno question on "odd" functions. kind hearted mathmatician needed? c: 10 points

Which function is an odd function?


f(x) = 0.8x^3

f(x) = 5x^2

f(x) = 0.7x^2 + 3

f(x) = 3x - 1

i completely appreciate anyones time that tries to help me out c:

Both other answers are right.
Deb has the key to testing for evenness/oddness of a function:
If f(-x) = f(x) for all x, then f is even.
If f(-x) = -f(x) for all x, then f is odd.
If f(-x) = neither of ±f(x) for all x, then f is neither even nor odd.

1. odd, because 0.8(-x)³ = -0.8x³
2. even, because 5(-x)² = 5x²
3. even, because 0.7(-x)² + 3 = 0.7x² + 3
4. neither even nor odd, because
3(-x) - 1 = -3x - 1 ≠ 3x - 1
3(-x) - 1 = -3x - 1 ≠ -(3x - 1) = -3x + 1

Additional info -- amaze your teacher: every function of x can be written as an even fn of x + an odd fn of x, with those two parts uniquely determined:
f(x) = E(x) + O(x), where
E(x) = ½[f(x) + f(-x)]
O(x) = ½[f(x) - f(-x)]

Using this, you can find the even and odd parts of that last function in your list, f(x) = 3x - 1

the first one is the odd function. A function is odd if it looks the same when reflected in the X-axis and then reflected in the y-axis if that helps you visualize it. A function is even when it looks the same reflected in the y-axis only. Therefore 2 and 3 are even. The last one is neither even nor odd.

f(x) = o.8x^3 is the odd function
as for odd function f(-x)= -f(x)
and for even function f(-x) = f(x)