Question 106931
even function are symmetric with respect to y-axis (f(-x) = f(x)).  Odd functions are symmetric with respect to origin (f(-x) = -f(x)).

So, take each function a substitute (-x) for x.

y=2x          =>  f(-x) = -2x.  Since f(-x) = -f(x) the function is odd.
y = 3x^3      =>  f(-x) = 3(-x)^3 = -3x^3  is odd
y = 5x^2 + 3  = > 5(-x)^2 + 3  = 5x^2 + 3 and is therefore even function.
y = 2x - 5    =>  2(-x) - 5 = -2x - 5  is nether odd nor even since f(-x) does not                
                              equal f(x) or -f(x).

NOTE:  Polynomials with all even exponents are even functions; polynomials with all odd exponents are odd functions.  However, you should use the f(-x) test when you are not dealing with polynomials.

Hope this helps.