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The graph of y = f(x) is as shown in th...

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.

Text Solution

Verified by Experts

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.
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