Question

Select all the toolkit functions below that are discontinuous

Answer 1

Three examples of discontinuous toolkit functions are the absolute value function, the step function, and the Dirichlet function.

Step-by-step explanation:

For a function to be discontinuous, it must have a point of discontinuity where the limit of the function does not exist or is not equal to the value of the function at that point. Here are three examples of toolkit functions that are discontinuous:

1. Absolute Value Function: The absolute value function, f(x) = |x|, is discontinuous at x=0 because the limit of the function does not exist at that point.
2. Step Function: The step function, f(x) = ⌊x⌋, where ⌊x⌋ is the greatest integer less than or equal to x, is discontinuous at each integer because the limit of the function does not exist at those points.
3. Dirichlet Function: The Dirichlet function, which is defined as 1 for rational numbers and 0 for irrational numbers, is discontinuous at every point because the limit of the function does not exist at any point.