1. **Problem Statement:** We want to find the domain of the function $f(x) = \frac{x^2}{x^2 + 4}$. The domain is the set of all $x$ values for which the function is defined. 2. **Key Rule:** A function with a denominator cannot have values that make the denominator zero because division by zero is undefined. 3. **Analyze the Denominator:** The denominator is $x^2 + 4$. Since $x^2 \geq 0$ for all real $x$, the smallest value of $x^2$ is 0. 4. **Minimum Value of Denominator:** When $x=0$, $x^2 + 4 = 0 + 4 = 4$, which is positive. 5. **Conclusion on Denominator:** Because $x^2 + 4$ is always at least 4 and never zero, the denominator never becomes zero. 6. **Domain Result:** Since there are no restrictions from the denominator, the function is defined for all real numbers. **Final answer:** The domain of $f(x)$ is $(-\infty, \infty)$, meaning all real numbers.