Final answer:
The minimum value of the function f(x) = |z+2|-1 is -1, occurring at z = -2. There is no maximum value, as f(x) increases indefinitely as the value of z moves further from -2.
Step-by-step explanation:
To find the maximum and minimum values of the function f(x) = |z+2|-1 for z being a real number, recall that the absolute value function, |z+2|, represents the distance from -2 on the real number line. The minimum value of this function is reached when z = -2, which will result in f(x) = 0 - 1 = -1. As z moves away from -2, whether to the left (negative direction) or to the right (positive direction), f(x) will increase accordingly. Therefore, there is no upper bound to the maximum value of f(x); it will continue to increase indefinitely as |z+2| gets larger.
The graph of this function would show a V-shaped curve with its vertex at the point (-2, -1) on the coordinate plane. The graph divides into two lines that extend up and out indefinitely to the left and right from the vertex, indicating the increase in f(x) as z moves away from -2.