Try to move the number “a” on the slider
(select it and then use the arrows on your keyboard).
Observe that when “a” reaches exactly the value 1,
the point P on the graph jumps above the point (1,2),
exactly as required by the definition of the function.

f(x) = If[x  <  1, x^(2), If[x ≟ 1, 2, x - 1]]
a = 0.35 (slider from 0 to 2, step 0.01)
P: (a, f(a))
Q: (1, 2)