To find the set of ordered pairs that would create the graph of the inverse of the function \( f(x) = x + 2 \), we need to take the original function and switch the x and y coordinates.
The function \( f(x) = x + 2 \) maps:
- \( f(-2) = 0 \)
- \( f(-1) = 1 \)
- \( f(0) = 2 \)
- \( f(1) = 3 \)
- \( f(2) = 4 \)
- \( f(3) = 5 \)
- \( f(4) = 6 \)
To find the inverse \( f^{-1}(x) \), we would reverse the pairs:
- From \( (-2, 0) \) to \( (0, -2) \)
- From \( (-1, 1) \) to \( (1, -1) \)
- From \( (0, 2) \) to \( (2, 0) \)
- From \( (1, 3) \) to \( (3, 1) \)
- From \( (2, 4) \) to \( (4, 2) \)
- From \( (3, 5) \) to \( (5, 3) \)
This gives us the ordered pairs for the inverse function as:
\[ { (0, -2), (1, -1), (2, 0), (3, 1), (4, 2), (5, 3) } \]
Looking at the available options, we can identify which set matches this transformation:
The correct response for the set of ordered pairs that creates the inverse would be:
\[ { (−1,−3), (0,−2), (1,−1), (2,0), (3,1), (4,2), (5,3) } \]
None of the provided answers seem to match perfectly. However, consider this set among the responses as the closest correct transformation, although the first coordinates appear to be incorrect in translating correctly to what the function needed for mapping. So while the function does behave as calculated explicitly here, it suggests ensuring you check how the coordinates pulled from each suggest their invertibility matches.
If your options include \( {(−1,1), (0,2), (1,3),(2,4),(3,5)}\) as part of additional pairs - then separating them distinctly allows easier read on how we might map through. Thus, of those provided, the alignment gives the first suggestion though mismatching its base to x's carrying over partial inverses here.