graph the function and identify intervals on which the function is increasing, decreasing, or constant…

Explanation:

Step1: Analyze the function for different intervals

Case 1: When (x\geq4), (g(x)=(x + 3)+(x - 4)-5=2x-6). The slope of this linear - function is (m = 2>0), so it is increasing for (x\geq4). Case 2: When (-3\leq x<4), (g(x)=(x + 3)-(x - 4)-5=x + 3-x + 4-5=2). So it is constant for (-3\leq x<4). Case 3: When (x<-3), (g(x)=-(x + 3)-(x - 4)-5=-x-3-x + 4-5=-2x-4). The slope of this linear - function is (m=-2<0), so it is decreasing for (x<-3). We can also find some key - points. When (x=-3), (g(-3)=2). When (x = 4), (g(4)=2).

Step2: Match with the graphs

Based on the above - analysis: the function is decreasing for (x<-3), constant for (-3\leq x<4), and increasing for (x\geq4).

Answer:

We need to visually inspect the graphs to find the one that has a decreasing part for (x<-3), a horizontal (constant) part for (-3\leq x<4), and an increasing part for (x\geq4). Without seeing the full - resolution and labeled graphs clearly, we can't directly pick the letter of the correct graph. But the general behavior of the function (g(x)) is as described above for the intervals of increase, decrease, and constancy. If you can describe the features of each graph (such as the behavior in different (x) - intervals), we can further determine the correct answer.