Question

Explain why the function is discontinuous at the given number a.

1) The function is not defined at a
2) The function has a jump discontinuity at a
3) The function has a removable discontinuity at a
4) The function is continuous at a

Answer 1

The answer explains the different types of discontinuities a function can have at a specific point, and how to determine them.

Step-by-step explanation:

The given options describe different types of discontinuities that can occur in a function at a specific point a. The correct option to choose depends on the specific behavior of the function at that point.

If the function is not defined at a, it means that the function does not have a value at that point. This results in a removable discontinuity.

If the function has a jump discontinuity at a, it means that the function has different values from the left and right sides of that point.

If the function is continuous at a, it means that the function does not have any abrupt changes or jumps at that point.