Final answer:
The function f(x) is neither even nor odd and thus has no particular symmetry concerning the y-axis or origin. The function g(x) is an odd function, implying it is symmetrical concerning the origin.
Step-by-step explanation:
To determine whether the functions f(x) = \frac{x^2 + 9}{x} and g(x) = x^3 - 4x are even, odd, or neither, we can test them against the definitions of symmetry for even and odd functions. An even function satisfies y(x) = y(-x), which means it is symmetric about the y-axis. To test this, we replace x with -x in the functions: f(-x) = \frac{(-x)^2 + 9}{-x} = \frac{x^2 + 9}{-x}, which does not equal f(x), thus f(x) is not even. g(-x) = (-x)^3 - 4(-x) = -x^3 + 4x, which is the negative of g(x), implying g(x) is odd. An odd function satisfies y(x) = -y(-x) and has symmetry about the origin. Again, let's check if our function f(x) is odd: Since f(-x) does not equal -f(x), function f(x) is not odd. Since f(x) is neither even nor odd, it has no particular symmetry concerning the y-axis or origin. However, as noted earlier, g(x) is odd, meaning it has rotational symmetry about the origin.