To determine which graph represents the rational function based on the provided table of values, we need to pay close attention to the characteristics outlined:
- The function is undefined at \( x = -2 \).
- The values for \( y \) at various \( x \) values suggest that as \( x \) approaches \( -2 \), there is a discontinuity (i.e., an asymptote or hole).
The key points from the table are:
- At \( x = -6, y = 0 \)
- At \( x = -5, y = 2 \)
- At \( x = -4, y = 5 \)
- At \( x = -2, y = \) undefined (discontinuity)
- At \( x = 0, y = -3 \)
- At \( x = 2, y = 2 \)
- At \( x = 4, y = 5 \)
Based on the description of the graphs, we should choose the graph that has a vertical asymptote or a hole at \( x = -2 \) and shows the correct behavior around this point.
From the options given in your prompt, both graphs with a dashed line at \( x = -2 \) would imply a discontinuity at that point, which aligns with the data you've provided.
However, since the data suggest \( x = -2 \) is undefined in your provided values and the validated points describe behavior away from that discontinuity, I would choose the graph that emphasizes a break at that point, showing curves on both sides while respecting other listed points in the table.
Therefore, the correct graph is the one with a dashed line at \( x = -2 \), with the left branch approaching 5 at \( x = -4 \) and the right branch curving through the other points, aligning closely with the given values.
Answer: The graph with a dashed line through \( (−2, 6) \) and \( (−2, −6) \).
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