Answer
See graph and explanations.
Work Step by Step
Step 1. Given $f(x)=\frac{3x-1}{x-2}$, we have $f(-x)=\frac{-3x-1}{-x-2}=\frac{3x+1}{x+2}$, no symmetry.
Step 2. Vertical asymptote: $x=2$
Step 3. Horizontal asymptote: $y=3$
Step 4. X-intercept: $x=\frac{1}{3}$
Step 5. Y-intercept: $f(0)=\frac{1}{2}$
Step 6. Use test points as necessary to graph the function as shown.