Use the Heaviside function as an on the switch over the interval [a,b].
Let the H(x) be the Heaviside function defined as a piece-wise function such that it is zero if x is less than zero, and 1 if it is greater than or equal zero. From that, we can use the Heaviside function as an on/off function, to represent piece-wise functions.
The Attempt at a Solution
I know that I can use H(x-a) where a is an element of the reals to indicate a horizontal translation of the Heaviside function. Similarly, I can write (H(x-a)-H(x-b)), where a and b are reals to denote an on the switch over the interval a<x<=b. If I was to reverse the position of "x" and "a", as well as "x" and "b", I could represent the "on" switch over the interval a<=x<b. However, I can't seem to represent the interval a<=x<=b. Where the endpoints are included.