The graph of y = f(x) is not continuous. This is because of the presence of jumps and holes
When is a function said to be continuous
A function is said to be continuous when there are no sudden jumps, breaks, or holes in its graph.
There are lots of holes in the function. Typical example is at (1, 0), (1, 3)... and just one whole makes the function unable to be continuous
A function can be continuous over an interval if it is continuous at every point within that interval. Continuous functions have smooth, unbroken graphs