\( \left. \begin{array} { l } { F ( x ) = \frac { 3 x ^ { 2 } - 2 x + 4 } { 4 x ^ { 2 } - 2 x } } \\ { g ( x ) = 5 x ^ { 4 } + 6 x ^ { 3 } } \end{array} \right. \)

Did you know that functions like \( F(x) \) and \( g(x) \) can represent real-world phenomena? For example, \( F(x) \) could model a physical system, such as the motion of an object where the terms in the equation account for different forces acting on it. Meanwhile, \( g(x) \), being a polynomial of higher degree, could represent things like population growth, where the terms suggest accelerating rates over time. When working with functions, it’s easy to overlook domain restrictions—especially with rational functions like \( F(x) \). Always check where the denominator equals zero, as those points will lead to undefined values in the function. For \( F(x) \), setting \( 4x^2 - 2x = 0 \) could help pinpoint restrictions on \( x \). This way, you'll avoid common pitfalls when analyzing the function's behavior!