\( 1 \leftarrow \quad \) Determine the domain of the function. \( f(x)=\frac{x^{2}}{12-x} \)

The domain of the function \( f(x) = \frac{x^{2}}{12 - x} \) consists of all real numbers except where the denominator equals zero. To find the restriction, set the denominator equal to zero: \( 12 - x = 0 \). This gives \( x = 12 \). Therefore, the domain is all real numbers except \( x = 12 \), or in interval notation, \( (-\infty, 12) \cup (12, \infty) \). Now, it's important to remember that when dealing with rational functions, always check for values that make the denominator zero, as they are the culprits for undefined behavior! In this case, just avoid \( x = 12 \) and you’re good to go!