Final answer:
The correct function represented by the graph is option C) –|x| + 3, as it has a positive value at x = 3 and a decreasing slope.
Step-by-step explanation:
The given graph has a positive value at x = 3 and a positive slope that is decreasing in magnitude with increasing x. Option C) –|x| + 3 could correspond to f(x) because it has a positive value at x = 3 and a decreasing slope. Let's analyze each option to determine the correct answer.
A) |–x + 3|: This function has a positive value at x = 3, but its slope is increasing in magnitude with increasing x, which does not match the given graph.
B) –|x + 3|: This function does not have a positive value at x = 3, so it does not match the given graph.
C) –|x| + 3: This function has a positive value at x = 3 and a decreasing slope, which matches the given graph.
D) |–x| + 3: This function does not have a positive value at x = 3 and a decreasing slope, so it does not match the given graph.
Therefore, the correct option is C) –|x| + 3.