mac1140_lecture17_2 - L17 3.5 Graphs of Relations and Functions A piecewise-defined function is a function defined by different rules over different

mac1140_lecture17_2 - L17 3.5 Graphs of Relations and...

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143 L17 §3.5 Graphs of Relations and Functions Continuity : A function is continuous over an interval of its domain if its hand-drawn graph over that interval can be sketched without lifting the pencil from the paper. The graph of a continuous function has no holes, jumps, or gaps. Example . Determine the largest open intervals over which each of the functions is continuous. a) b) 144 A piecewise-defined function is a function defined by different rules over different parts of the domain. To sketch the graph of a piecewise function : 1. Divide the domain of the function into parts according to the rules. 2. Plot each branch separately. 3. On each part of the graph, draw endpoints as a if they are to be included and a D if they are not to be included. (Symbol D indicates a hole on the graph.) Example . Sketch 3 if 1 2 if 1 1 2 1 if 1 x x y x x x + ≤ − = < >