\[ f(x)=\frac{8 x^{5}-6 x^{3}+4 x}{7 x^{2}+4} \] Part: \( \mathbf{0} / \mathbf{2} \) Part 1 of 2 (a) Determine if the function is even, odd, or neither. The function is neither odd nor even. The function is even. The function is odd.

To determine whether the function \( f(x) = \frac{8 x^{5}-6 x^{3}+4 x}{7 x^{2}+4} \) is even, odd, or neither, we should evaluate \( f(-x) \). Calculating \( f(-x) \): \[ f(-x) = \frac{8 (-x)^{5} - 6 (-x)^{3} + 4 (-x)}{7 (-x)^{2} + 4} = \frac{-8 x^5 + 6 x^3 - 4 x}{7 x^2 + 4} \] Now, compare \( f(-x) \) with \( f(x) \): 1. **Even function**: If \( f(-x) = f(x) \). 2. **Odd function**: If \( f(-x) = -f(x) \). Simplifying \( -f(x) \): \[ -f(x) = -\frac{8 x^{5}-6 x^{3}+4 x}{7 x^{2}+4} = \frac{-8 x^{5} + 6 x^{3} - 4 x}{7 x^{2}+4} \] Since \( f(-x) = -f(x) \), we conclude that the function is **odd**.