See graph and explanations.
Work Step by Step
Step 1. Given $f(x)=(x-1)^2(x-3)$, we can identify two zeros $x=1$ with multiplicity 2 and $x=3$ Step 2. The curve with touch the x-axis and reflect at $x=1$ and cross the x-axis at $x=3$ Step 3. The y-intercept can be found at $y=(0-1)^2(0-3)=-3$ Step 4. The end behaviors can be found as $x\to-\infty,y\to-\infty$ and $x\to\infty,y\to\infty$ Step 5. Using test points to examine the signs across the zeros, we have $...(-)...(1)...(-)...(3)...(+)...$ Step 6. We can not find any symmetry of the function. Step 7. Use the above results to graph the function as shown in the figure.