Chapter 3 - Polynomial and Rational Functions - 3.5 Rational Functions: Graphs, Applications, and Models - 3.5 Exercises - Page 378: 103

$f(x)=\frac{x-2}{(x)(x-4)}$

Step 1. From the given graph, we can identify: V.A. $x=0,4$, H.A. $y=0$, Step 2. Thus, a possible rational function can be written as $f(x)=\frac{x+k}{(x)(x-4)}$ where $k$ is unknown. Step 3. Use the zero at $f(2)=0$, we have $\frac{2+k}{(2)(2-4)}=0$ which gives $k=-2$ Step 4. Thus $f(x)=\frac{x-2}{(x)(x-4)}$