Q:

# How do you graph a piecewise-defined function?

A:

Graphing a piecewise-defined function is a process that takes a variable amount of time depending on the complexity and scale of the function being graphed. You need graphing paper and a pencil.

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1. Graph all of the closed end points

Find all of the points where the piecewise function transfers from one function to the next. At these points, examine the inequalities of the piecewise function to see which functions these points will lay in. Plug the value of each point into the correct function, and draw a filled-in bubble at each spot.

2. Draw the open end points

Return to the closed end points, and find the second, unused functions. Plug the same points into these functions. At these points, draw circles, but don't fill them in. An unfilled circle denotes an open end point.

3. Fill the spaces between end points with graphed functions

Consider using a calculator to solve for the graphing shapes of each of the constituent functions in your piecewise function. Draw these functions in the appropriate regions to connect the gaps between different open and closed end points. Make sure the shape is appropriate for the scale and location on the graph where each function is located.

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