Question: H is the Heaviside function, defined by In each case, sketch the graph of , indicate whether or not is continuous, andif is

H is the Heaviside function, defined by

H(x) 6 0 when x < 0 1 when x 0

In each case, sketch the graph of ƒ, indicate whether or not ƒ is continuous, and—if ƒ is not continuous—identify the points of discontinuity.

(a) f(x) = H(x)(x + 1) (b) f(x) = H(x)x (c) f(x) = (d) f(x) = H(1+x)H(1-x)(1-x) H(x - 2)x

H(x) 6 0 when x < 0 1 when x 0

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