it depends on the domain. Between -1 and +4, the function is continuous (I think of a continuous function as one where I do not have to take my hand off the paper when I draw it). But outside the above domain, it is not. Since it is not even defined there. So when you ask if a function is continuous, you have to also say over what range. May be Wolfram alpha has a command to also tell it the range?
The derivative of the function, however, is not continuous, since there is a jump at x=3.