Work out continuity checker instantly with clear inputs, formula shown and shareable results.
A function is continuous at a point when it is defined there, the limit exists, and the two agree. A rational function fails only where the denominator vanishes, and there the failure is removable if the numerator vanishes too.
Continuity
f is continuous at a ⇔ f(a) exists and lim(x→a) f(x) = f(a)
The denominator factors as (x − 4)(x + 2), so the factor cancels and the discontinuity is removable with limit 1/6.
One where both one-sided limits exist but differ, as in a piecewise definition or the step function.