How can f(0.8) = 0.8? The value of f at this point is clearly 0. (That's what the red dot is telling you.)

From the left, I get that lim f(0.8) is about -0.6 and from the right I get that lim f(0.8) is about -1.1. Since these limits are not the same, the function is not continuous at this point.

-Dan