**Step 1:**
To sketch the graph of the function \(f(x)\), we need to consider the different cases given:
- For \(x < -2\), \(f(x) = 14\)
- For \(-2 < x < 7\), \(f(x) = -x + 12\)
- For \(x = 7\), \(f(x) = 7\)
- For \(x > 7\), \(f(x) = 12\)
**Step 2:**
Now, let's
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