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all right what id like to show you guys is when given a piecewise function how to write actually um what the function is so how to write it piecewise how to write a piecewise function from a graph all right first of all what you guys what we need to do is we need to determine what are three equations because you have three different lines all with different constraints so we need to determine what are three equations so uh what im going to go ahead and do is im just going to start left to right i look at this line all right this is a straight constant line at six so i know when i do not have when i have a straight line i have no slope therefore my slope would be zero so therefore this is just going to be a constant term and the constant term i know if i was to continue this line with no constraints it would cross at 6. so therefore this line is y equals 6. thats how you graph that line then i look at the next one if i pretend this graph had no constraints i could continue this infi