To find the integer values of $x$ where the limit does not equal a finite value as $x$ approaches those values, let's analyze the described graph step-by-step.

1. Discontinuities due to open points:

   • The graph has open points at $(-2, -4)$, $(-1, -1)$, and $(1, -1)$. However, open points alone do not necessarily indicate that the limit does not exist. We need to consider other factors such as jumps or vertical asymptotes.

2. Non-continuous closed point:

   • There is a closed point at $(-1, -2)$, but the graph reaches the open point $(-1, -1)$. This suggests a jump discontinuity at $x = -1$, because the function jumps from $(-1, -1)$ to $(-1, -2)$. At jump discontinuities, the left-hand and right-hand limits differ, meaning the overall limit does not exist at $x = -1$.

3. Asymptote at $x = 3$:

   • The graph approaches vertical asymptotes as $x$ approaches 3 from both the left and the right, going toward $\infty$ and $-\infty$, respectively. This implies that the limit does not exist at $x = 3$, since the function does not approach a finite value.

Conclusion:

The integer values of $x$ where the limit does not equal a finite value are:

• $x = -1$ (due to the jump discontinuity)
• $x = 3$ (due to the vertical asymptote)

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Would you like more details about this process or further clarification? Here are five follow-up questions you might find interesting:

1. What are the different types of discontinuities in a graph?
2. How do we determine if a limit exists at a point of discontinuity?
3. How do asymptotes affect the existence of limits?
4. Can a function have a limit at an open point?
5. How do we interpret left-hand and right-hand limits on a graph?

Tip: When analyzing graphs for limits, always check for discontinuities, jumps, holes, and vertical asymptotes, as these often indicate where limits do not exist.