In this section we will work a couple of examples involving limits, continuity and piecewise functions. Recall that a function {{MATH_29}} is continuous at a point {{MATH_30}} if {{MATH_31}}. This gave the {{CMD_32}}continuity checklist{{CMD_33}}. To determine whether a function {{MATH_34}} is continuous at a point {{MATH_35}}, we must check that: {{CMD_36}} {{CMD_37}} {{CMD_38}} {{MATH_39}} is defined, {{CMD_40}} {{CMD_41}} {{MATH_42}} exists, and then {{CMD_43}} {{CMD_44}} {{MATH_45}}. {{CMD_46}} In this section, since we are dealing with piecewise-defined functions, we may have to consider one-sided limits when determining if item {{CMD_47}} holds for our function. However, item {{CMD_48}} does not mention one-sided limits. When using the checklist to justify the continuity of a function, take care to mention the specific conditions that are required.