To determine which ordered pair can be added to the existing points without violating the definition of a function, we need to understand that a function cannot have more than one output (y-value) for the same input (x-value).
The existing points are:
- \((-3, 1)\)
- \((-2, -2)\)
- \((1, 2)\)
- \((2, -3)\)
Now, we check the x-values of the given points:
- The x-values are: \(-3\), \(-2\), \(1\), and \(2\).
For the new ordered pair to be added, its x-value must not match any of the existing x-values; otherwise, it would produce more than one y-value for that x-value, which would mean it is not a function.
Thus, valid x-values for the new ordered pair must be anything except \(-3\), \(-2\), \(1\), or \(2\). Let's say we choose, for example, \(0\) as the x-value. We could pair it with any y-value.
So, one possible ordered pair that can be added is \((0, y)\) where \(y\) can be any real number (it could be \(0\), \(3\), etc.). This way, the graph will still represent a function.
In conclusion, any ordered pair with an x-value different from \(-3\), \(-2\), \(1\), and \(2\) can be plotted without violating the function rule. For example, \((0, 5)\) would be valid.
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