Graphing a piecewise function

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Question from Shanti, a student:

how do you graph a step function or piecewise function such as
u^2 if u is greater than or equal to -2 and less than 1
2- u if u is greater than or equal to 1 and less than 4

Hi Shanti,

I would start by sketching both graphs y = u² and y = 2 - u making sure that I covered the entire range of the u-values, -2 to 4.

both graphs

y = u² and y = 2 - u

But you only want pieces of these graphs. The piece of the parabola y = u² for u between -2 and 1,

the parabols

and the piece of the line y = 2 - u for u between 1 and 4.

the line

Hence removing the unwanted pieces from the graph containing both equations I get

The piecewise graph

equation

I hope this helps,
Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.