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

$h(x)=\frac{x^2-16}{x-4}$

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

$\frac{x^2-16}{x-4}\text{ is a polynomial , it is a continuous function }$

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.