Quoted By:
a) It is not.
b) It is.
Continuity just means that if you make an arbitrarily small move in the x direction there will also only be a tiny move in the y direction. Or in layman's terms: You can draw the function without lifting the pen.
I'm just an interested hobbyist, so don't ask me for a strict mathematical proof, but I would simply look whether continuity is plausible.
For a) you know the point (0, 1), so check the y at x = -0.01 and at x = 0.01 and you'll find out that both have y = 1.99997, which is far away from y = 1 (continuity would be with y = 2).
For b) do the same around (2, -2). x = 1.99 means y = -2.01 and x = 2.01 means y = -2.01. y = -2 is right between the two values which is exactly what you'd expect for a linear function, meaning the point (2, -2) closes continuity.
Quick plot for visualisation included.
