1. **State the problem:** Find the horizontal and vertical asymptotes of a given function. 2. **General rules:** - Vertical asymptotes occur where the function is undefined, typically where the denominator is zero and the numerator is not zero. - Horizontal asymptotes describe the behavior of the function as $x \to \pm \infty$. 3. **Formula for vertical asymptotes:** Solve for $x$ in the denominator where it equals zero. 4. **Formula for horizontal asymptotes:** Evaluate the limit $\lim_{x \to \pm \infty} f(x)$. 5. **Example:** Suppose the function is $f(x) = \frac{2x+3}{x-1}$. 6. **Find vertical asymptote:** Set denominator equal to zero: $$x - 1 = 0 \implies x = 1$$ So, vertical asymptote is $x=1$. 7. **Find horizontal asymptote:** Since degrees of numerator and denominator are equal (both 1), horizontal asymptote is ratio of leading coefficients: $$y = \frac{2}{1} = 2$$ 8. **Answer:** Vertical asymptote at $x=1$, horizontal asymptote at $y=2$. This method applies to rational functions generally.