The graph of ` y = f(x)` is as shown in the following figure. Identify the points of discontinuity and give the reason for the same.

The graph of ` y = f(x)` is as shown in the following figure. Identify

1.	The graph of ` y = f(x)` is as shown in the following figure. Identify the points of discontinuity and give the reason for the same.
Answer» y = f(x) is discontinuous at x =- 3 as the value of the function is missing at this point. Assigning proper value to f(-3) [from the graph f(-3) = 2], f(x) can be made continuous at this point. y = f(x) is discontinuous at x = 0 as there is a jump in the value of the function at this point. Here ` underset(x to 0^(-))"lim" f(x) and underset(x to 0^(+))"lim" f(x) = 3`. At this point, the function cannot be made continuous. At x = 2, the function is discontinuous as the value of the value of the function is not same as the limiting value of function. That is, ` underset(x to 2) " lim" f (x) = 1` (limit of the function exists), but f(2) =- 1. At x = 6, the function is discontinuous as the value of the function is decreasing indefinitely when x is approached from either its left or its right.