1. The problem asks to identify all values of $x$ where the limit of the function $f(x)$ does not exist. 2. Limits do not exist at points where the function has vertical asymptotes, jump discontinuities, or oscillates without settling to a value. 3. From the graph description, there are vertical asymptotes near $x=3$ and $x=7$. At these points, the function values approach infinity or negative infinity from either side, so the limit does not exist. 4. There is also an open circle near $x=-1$, $y=-3$, indicating a removable discontinuity or a point where the function is not defined. The limit at $x=-1$ may still exist if the left and right limits are equal. 5. Since the graph does not mention a jump or oscillation at $x=-1$, and only an open circle is present, the limit at $x=-1$ likely exists. 6. Therefore, the values of $x$ where the limit does not exist are $x=3$ and $x=7$ due to vertical asymptotes. Final answer: The limit of $f(x)$ does not exist at $$x=3 \text{ and } x=7.$$