To determine if the relation shown in the table is a function, we need to check whether every input (x-value) corresponds to exactly one output (f(x)).
In the provided table:
- When \( x = 3 \), \( f(x) = 2 \)
- When \( x = 0 \), \( f(x) = 1 \)
- When \( x = 5 \), \( f(x) = -7 \)
- When \( x = -3 \), \( f(x) = 2 \)
Here, the input \( 3 \) maps to \( 2 \), \( 0 \) maps to \( 1 \), \( 5 \) maps to \( -7 \), and \( -3 \) also maps to \( 2 \).
The key observation is that while the input \( -3 \) yields the same output \( 2 \) as the input \( 3 \), each input still has one unique output. Therefore, there are no repeated inputs producing different outputs, and thus, there are no violations of the definition of a function.
Based on this reasoning, the correct answer is:
D. Yes, every input has one unique output.