\begin{tabular}{l} What is the domain of \( f(x)=9-x^{2} ? \) \\ \( \mathbf{f}(\mathrm{x}) \geq \mathbf{9} \quad \) All real numbers \\ \hline\end{tabular}

The function \( f(x) = 9 - x^2 \) is a downward-opening parabola that reaches its maximum value at the vertex, which is at \( x = 0 \). Therefore, this function will have real values for all \( x \); you can plug in any real number and get a corresponding output. So the domain of \( f(x) \) is indeed all real numbers, denoted as \( (-\infty, \infty) \). To visualize this, think of it as the path of a ball thrown upwards: it rises to a peak (the maximum point at \( (0, 9) \)) and then starts to fall back down, but every single throw represents a real number achievable by some angle or force! Thus, no restrictions limit \( x \) in this equation.