Answer
See graph and explanations.
Work Step by Step
Step 1. Rewrite the function as $f(x)=\frac{x^2-x+3x-3+4}{x-1}=x+3+\frac{4}{x-1}$
Step 2. We can identify a vertical asymptote as $x=1$
Step 3. Slant asymptote $y=x+3$
Step 4. The x-intercept is $x=-1$
Step 5. The y-intercept is $y=-1$
Step 6. There is no horizontal asymptote.
Step 7. Use test points as necessary to graph the function as shown in the figure.
