I was out on Thursday at a leadership meeting so on Friday, we graphed piecewise functions that didn't look like straight lines, using graphs from the quadratic, cubic, radical, and exponential function families. We use exactly the same process as we do for graphing linear functions: graph both graphs, graph the asymptote, and determine which part of which graph goes on the right and left side of the asymptote.
There are only two things that we need to keep in mind when graphing nonlinear piecewise functions:
1) Unlike linear functions, both nonlinear functions don't have to touch the asymptote
2) Unlike linear functions, both nonlinear functions don't have to show up on the graph. Sometimes, only one graph will be present.
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