Final answer:
The limit of the greatest integer function as x approaches -2 from the left is -3, since the function will map to the largest integer less than -2.
Step-by-step explanation:
The question is related to the evaluation of the limit of the greatest integer function as x approaches -2 from the left. This function, also known as the floor function, maps a real number to the greatest integer less than or equal to that number. To evaluate the limit as x approaches -2, we consider the value that the greatest integer function is approaching. As we approach -2 from the left side (which means values that are just smaller than -2), the greatest integer function will give the value of -3, because -3 is the greatest integer that is less than any number in the interval (-3, -2). Therefore, the limit of the greatest integer function as x approaches -2 from the left, denoted as limx→-2- ➦x➧, is -3.
To provide an answer to the typo-ridden question provided by the student, it is important to correct the notation and ask for any graphs referenced if they are necessary to solving the problem. Without the graph or correct description, it's impossible to evaluate the limit accurately.