1. **State the problem:** We are given the function $f(x) = x^{-2}$ and need to understand its behavior. 2. **Recall the formula and rules:** The function $f(x) = x^{-2}$ can be rewritten using the negative exponent rule: $x^{-n} = \frac{1}{x^n}$. So, $f(x) = \frac{1}{x^2}$. 3. **Analyze the function:** Since $x^2$ is always positive for $x \neq 0$, $f(x)$ is always positive except at $x=0$ where it is undefined. 4. **Domain:** The function is defined for all real numbers except $x=0$. 5. **Behavior near zero:** As $x$ approaches 0 from either side, $f(x)$ approaches infinity. 6. **Behavior at infinity:** As $x$ approaches $\pm \infty$, $f(x)$ approaches 0. 7. **Summary:** The function $f(x) = x^{-2}$ is equivalent to $f(x) = \frac{1}{x^2}$, positive everywhere except undefined at zero, with vertical asymptote at $x=0$ and horizontal asymptote at $y=0$.