Question

Use a graphing utility to graph the function. use the graph to determine any x - values at which the function is not continuous.

Answer 1

Step 1 :

The function is

Graph the function :

Observe the graph,

Non-removable discontinuity at :

There is not way to ' plug the hole ' or redefine the function at only one point so that the result is continuous.

The domain of  is all nonzero real numbers and  is continuous at every - value in its domain.

But, at , the function  is not continuous or is undefined, and cannot be made continuous by being a new value at .

Thus, at , the function  has a nonremovable discontinuity.

Solution :

At , the function  has a nonremovable discontinuity.