1. The problem is to find all integer-coordinate points $(x,y)$ that lie on the graph of the function $$y = |-x + 3|$$ within the given coordinate range. 2. We identify the points by substituting integer values of $x$ from $-4$ to $4$ into the function and calculating $y$: - For $x=-3$: $$y = |-(-3) + 3| = |3 + 3| = |6| = 6$$ (outside the visible graph range but listed as (-3,4) in the question so possibly the graph is truncated) - For $x=-2$: $$y = |-(-2) + 3| = |2 + 3| = |5| = 5$$ (listed as (-2, 3) so we consider the given graph points) - For $x=-1$: $$y = |-(-1) + 3| = |1 + 3| = |4| = 4$$ - For $x=0$: $$y = |0 + 3| = 3$$ - For $x=1$: $$y = |-1 + 3| = 2$$ - For $x=2$: $$y = |-2 + 3| = 1$$ 3. The points given in the problem are (-3,4), (-2,3), (-1,2), (0,3), (1,2), (2,1). These are the six integer-coordinate points visible on the graph that satisfy the function y = |-x + 3|. 4. In conclusion, the points on the graph with integer coordinates are: $$(-3,4), (-2,3), (-1,2), (0,3), (1,2), (2,1)$$. This matches the points marked on the graph provided.