Final answer:
A discontinuous function can have a Laplace transform, with the Heaviside step function being a classic example of a discontinuous function with a well-defined Laplace transform.
Step-by-step explanation:
True or False: Can a discontinuous function have a Laplace transform? The correct answer is True. Discontinuous functions can indeed have Laplace transforms. The Laplace transform is quite powerful as it deals with a class of functions which includes discontinuities, given they adhere to certain conditions such as being piecewise continuous and of exponential order.
The presence of a discontinuity does not necessarily prevent a function from having a Laplace transform. For example, the Heaviside step function is discontinuous but has a well-defined Laplace transform. The ability to handle discontinuities is, in fact, one of the significant advantages of using the Laplace transform in engineering and science to solve differential equations.