When x<-2 |x+2| becomes 2-x; when x>-2 |x+2| becomes x+2. So x=-2 is a point to note on a graph. The graph of 2-x has negative slope (\) while x+2 has positive slope. So the graph resembles a V shape with the point of the V at (-2,0), and a y intercept at 2, when x=0. But the limits |x+2|<3 restrict the graph. Draw a line parallel to the x axis at y=3. This line reduces the V to an isosceles triangle with vertices at (-5,3), (1,3) and (-2,0). The domain of x is -5<x<1, and the range of y=|x+2| for y<3 is 0<y<3. The truncated V shape still represents the value of the function, showing |x+2| between the limits for x of -5 to +1.
a. The domain of x is all real values between -5 and +1 inclusive.
b. The domain is discontinuous consisting of the set of integers {-5 -4 -3 -2 -1 0 1 }. The corresponding set of |x+2| values is { 3 2 1 0 1 2 3 }.
c. The domain is between 0 and 1 inclusive and continuously.