1. **State the problem:** We are given the function $f(x) = \frac{1}{x} - 2$ and want to understand its behavior. 2. **Rewrite the function:** The function can be written as a single rational expression: $$f(x) = \frac{1}{x} - 2 = \frac{1 - 2x}{x}$$ 3. **Domain:** The function is undefined where the denominator is zero, so $x \neq 0$. 4. **Intercepts:** - **y-intercept:** Set $x=0$ but this is not allowed, so no y-intercept. - **x-intercept:** Set $f(x) = 0$: $$\frac{1 - 2x}{x} = 0 \implies 1 - 2x = 0 \implies x = \frac{1}{2}$$ 5. **Asymptotes:** - Vertical asymptote at $x=0$ (denominator zero). - Horizontal asymptote as $x \to \pm \infty$: $$\lim_{x \to \pm \infty} f(x) = \lim_{x \to \pm \infty} \left(\frac{1}{x} - 2\right) = -2$$ 6. **Summary:** The function has a vertical asymptote at $x=0$, a horizontal asymptote at $y=-2$, and an x-intercept at $x=\frac{1}{2}$. **Final answer:** $$f(x) = \frac{1 - 2x}{x}, \quad x \neq 0$$ Intercept: $\left(\frac{1}{2}, 0\right)$ Vertical asymptote: $x=0$ Horizontal asymptote: $y=-2$