The Heaviside function (named after Oliver Heaviside, 1850–1925) is defined by:

The Heaviside function can be used to “turn on” another function at a specific value in the domain, as seen in the four examples here. For each of the following, sketch the graph of ƒ.
(a)ƒ(x) = H(x)x²
(b) ƒ(x) = H(x)(1 − x²)
(c) ƒ(x) = H(x − 1)x
(d) ƒ(x) = H(x + 2)x²

H(x) = (0 1 when x < 0 when x 0