To determine the correct range for the graph described, we first need to identify the coordinates involved in the segments.
The first segment goes from the point \((-5, -2)\) to the point \((0, -1)\), and the second segment goes from \((0, -1)\) to \((2, 3)\).
Now, let's examine the \(x\) and \(y\) values for each point:
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The points on the first segment are:
- \((-5, -2)\) (with \(x = -5\), \(y = -2\))
- \((0, -1)\) (with \(x = 0\), \(y = -1\))
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The points on the second segment are:
- \((0, -1)\) (with \(x = 0\), \(y = -1\))
- \((2, 3)\) (with \(x = 2\), \(y = 3\))
Now we find the ranges for \(x\) and \(y\):
For \(x\):
- The lowest value of \(x\) from the points is \(-5\) (from \((-5, -2)\)).
- The highest value of \(x\) is \(2\) (from \((2, 3)\)).
- Therefore, the range for \(x\) is: \[-5 \leq x \leq 2\]
For \(y\):
- The lowest value of \(y\) from the points is \(-2\) (from \((-5, -2)\)).
- The highest value of \(y\) is \(3\) (from \((2, 3)\)).
- Therefore, the range for \(y\) is: \[-2 \leq y \leq 3\]
Now, let's match these ranges with the provided options:
- \(-5 \leq x \leq 2\) (correct for \(x\))
- \(-5 \leq y \leq 2\) (incorrect for \(y\))
- \(-2 \leq x \leq 3\) (incorrect for \(x\))
- \(-2 \leq y \leq 3\) (correct for \(y\))
Thus, the correct ranges are:
- For \(x\): \(-5 \leq x \leq 2\)
- For \(y\): \(-2 \leq y \leq 3\)
However, if the question asks for "the correct range for the graph," and since only one option is typically expected in such cases, the answer based on the \(x\) range is: −5 ≤ x ≤ 2.