To determine the correct range for the graph depicted by the points given, we need to evaluate the y-values represented by those points.
- The points provided are:
- From \((-4, -2)\) to \((0, -1)\)
- From \((0, -1)\) to \((3, 5)\)
Now we will extract the y-values from these points:
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The y-values from the first segment, from point \((-4, -2)\) to \((0, -1)\), are:
- \(-2\) (from the point \((-4, -2)\))
- \(-1\) (from the point \((0, -1)\))
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The y-values from the second segment, from point \((0, -1)\) to \((3, 5)\), are:
- \(-1\) (from the point \((0, -1)\))
- \(5\) (from the point \((3, 5)\))
Now we can identify the minimum and maximum y-values across both segments:
- The minimum y-value is \(-2\) (the lowest point from the first segment).
- The maximum y-value is \(5\) (the highest point from the second segment).
Thus, the range of the y-values is: \[ -2 \leq y \leq 5 \]
Next, we also need to consider the x-values which progress as follows:
- The x-values from the first segment range from \(-4\) to \(0\).
- The x-values from the second segment range from \(0\) to \(3\).
The overall x-range therefore is from: \(-4\) (the x-value from the first segment) to \(3\) (the x-value from the second segment).
Thus, the range of x-values is: \[ -4 \leq x \leq 3 \]
Given the options you provided, we have determined:
- For y-values: \(−2 ≤ y ≤ 5\)
- For x-values: \(−4 ≤ x ≤ 3\)
The correct answers based on the y-values is: \(-2 ≤ y ≤ 5\)
Therefore, the final answer is: −2 ≤ y ≤ 5.