Mathematics - Calculus - Pre-Calculus - Continuity - Fix the Discontinuity

Show piecewise functions with removable discontinuities (holes). The student adjusts a slider or types a value to 'fill the hole'. Example: f(x) = (x²-1)/(x-1) for x≠1, and f(1) = ? Student tries values for f(1). When they set f(1)=2, the function becomes continuous (the hole fills). Show 4 examples