First, find the left-hand limit as x approaches the joining point 'a' from values less than a, and the right-hand limit from values greater than a. The function is continuous at 'a' only if both these limits are equal to each other and also equal to f(a).
I say this because checking from both sides feels like painting my feni lamps – you have to prepare both surfaces, the inside and the outside, evenly for the light to shine through properly. If one side is not done right, the whole piece won't hold together, just like the graph will break at that point. God bless, study well.
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