#Graphing piecewise function
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First, you can draw the vertical lines x = 1, x = 4.
Then, draw y = 3x - 5, but keep the part only to the left of x = 1.
Then, draw y = -2x + 3, but keep the part only between x = 1 and x = 4.
Then, draw y = 2, but keep the part only to the right of x = 2.
Finally, make sure to mark the correct points at the boundaries of the pieces.