## Precalculus (6th Edition) Blitzer

vertical asymptote $x=-2$ horizontal asymptote $y=1$ no slant asymptote. See graph.
Step 1. Factor the numerator and the denominator; we have $h(x)=\frac{x^2+4x+3}{(x+2)^2}=\frac{(x+3)(x+1)}{(x+2)^2}$ and there are no common factors. Step 2. The vertical asymptote can be found as $x=-2$ Step 3. The horizontal asymptote can be found when $x\pm\infty$ and we get $y=1$ Step 4. A slant asymptote exists if the numerator is one order higher than the denominator; for the given rational function, there is no slant asymptote. Step 5. See graph.