Answer
$f(x)=\frac{x^2-x-2}{x-1}$
Work Step by Step
Step 1. With a vertical asymptote of $x=1$; we can write part of the function as $f(x)=\frac{1}{x-1}$
Step 2. With a slant asymptote of $y=x$, we can modify the function as $f(x)=x+\frac{1}{x-1}=\frac{x^2-x}{x-1}$
Step 3. To get a y-intercept at 2, we modify the function as $f(x)=\frac{x^2-x-2}{x-1}$
Step 4. Checking the above function for the x-intercept, we have $x=-1,2$
Step 5. Thus, one possible answer is
$f(x)=\frac{x^2-x-2}{x-1}$
