Continuity of piecewise functions{{CMD_1}}{{PREAMBLE_2}}{{CMD_3}} {{CMD_4}} Here we use limits to check whether piecewise functions are continuous. {{CMD_5}} {{CMD_6}} Before we start talking about continuity of piecewise functions, let's remind ourselves of all famous functions that are continuous on their domains. {{CMD_7}}{{CMD_8}}{{CMD_9}} The following functions are continuous on their natural domains: {{CMD_10}} {{CMD_11}} Constant functions {{CMD_12}} {{CMD_13}} Polynomials {{CMD_14}} {{CMD_15}} Rational functions {{CMD_16}} {{CMD_17}} Power functions {{CMD_18}} {{CMD_19}} Exponential functions {{CMD_20}} {{CMD_21}} Logarithmic functions {{CMD_22}} {{CMD_23}} Trigonometric functions{{CMD_24}} {{CMD_25}} Inverse trigonometric functions {{CMD_26}} {{CMD_27}} In essence, we are saying that the functions listed above are continuous wherever they are defined.