Discuss the continuity of the function

Question

f(x)= {x^2-x-2/x+1 where x<-1

2x+2 where x>or equal to -1}

Answer 1

Graphing it you can see that the function is not continuous; it has a jump at x = 1:

If you plug in x = 1 to the "2x + 2" you get f(1) = 4. And the limit as x approaches 1 from the left is -2 (the value of "x² - x - 2" at x = 1 is -2).