A discontinuous function occurs when there is no y-value for a given x. So it matters how x is defined. Typically in a math textbook they'll say something like

x is an element in the set of real numbers.

This means that x can take on any real number value. Since the problems definition limited the y-values for a specific range of x-values and if the textbook says x can take on any real number value, then there is a range of x's that have discontinuous y-values. Namely for those that are not defined (when x<=-1). But it depends on the assumptions the book makes.