Chapter 3 - Polynomial and Rational Functions - 3.5 Rational Functions: Graphs, Applications, and Models - 3.5 Exercises - Page 378: 101

$f(x)=\frac{(x-3)(x+2)}{(x-2)(x+2)}$

Step 1. From the given graph, we can identify: V.A. $x=2$, H.A. $y=1$, hole $(-2,5/4)$ Step 2. Thus, a possible rational function can be written as $f(x)=\frac{(x+k)(x+2)}{(x-2)(x+2)}$ where $k$ is unknown. Step 3. For the hole $f(-2)=5/4$, we have $\frac{(-2+k)}{(-2-2)}=5/4$ which gives $k=-3$ Step 4. Thus $f(x)=\frac{(x-3)(x+2)}{(x-2)(x+2)}$