Answer
See graph and explanations.
Work Step by Step
Step 1. Given $f(x)=\frac{3x-1}{x-1}$, we test for symmetry,
$f(-x)=\frac{-3x-1}{-x-1}=\frac{3x+1}{x+1}$, so no symmetry.
Step 2. Identify vertical asymptotes: $x=1$
Step 3. Identify horizontal asymptotes: $y=3$
Step 4. Find x-intercepts: $x=\frac{1}{3}$
Step 5. Find y-intercepts: $f(0)=1$
Step 6. Using test points as necessary, we graph the function as shown in the figure.
