Chapter 3 - Polynomial and Rational Functions - 3.5 Rational Functions: Graphs, Applications, and Models - 3.5 Exercises - Page 378: 102

$f(x)=\frac{(x+1)(x-2)}{(x+3)(x-2)}$

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