1. The problem asks to identify which correspondences between sets are functions and justify why. 2. Recall the definition of a function: each element in the domain (set A) must be associated with exactly one element in the codomain (set B). 3. Analyze Graph 1: - Set A = {1, 2}, Set B = {3, 4} - Arrows: 1 \to 3, 2 \to 4 - Each element in A maps to exactly one element in B. - Therefore, Graph 1 represents a function. 4. Analyze Graph 2: - Set A = {1, 2}, Set B = {3} - Arrows: 1 \to 3, 2 \to 3 - Each element in A maps to exactly one element in B. - Therefore, Graph 2 represents a function. 5. Analyze Graph 3: - Set A = {2}, Set B = {3, 4} - Arrows: 2 \to 3, 2 \to 4 - Element 2 in A maps to two different elements in B. - This violates the definition of a function. - Therefore, Graph 3 does not represent a function. Final answer: - Graph 1 and Graph 2 correspondences are functions. - Graph 3 correspondence is not a function.