Question

Find and classify the discontinuities of the following function as removable or nonremovable. If aclassification has no discontinuities, write None for your answer.

Answer 1

The given function is

`h(x)=(x^2-16)/(x-4)`

The graph of the function is

here

`x^2-16\text{ is a polynomial , it is a continuous function }`

`x-4\text{ is a polynomial , it is a continuous function }`

Hence we know that

`(x^2-16)/(x-4)\text{ is a polynomial , it is a continuous function }`

From the graph, there is no break in the line of the function.

hence the given function is continuous everywhere

The function h(x) does not have any discontinuities.