Saturday, September 29, 2012

When having to graph a piecewise function, look at each piece separately, making sure to be careful with the restrictions on the variable.

For example,

3x - 2,  x less than or equal to -1
f(x) =
-2x + 4, x greater than -1

Graph 3x - 2 first, noting that the largest value that can be used for x is -1. So put -1 in for x to get the endpoint.  When doing so, see that f(-1) = (3)(-1) - 2 = -5.  Place the coordinate (-1, -5) on the graph. Then use the slope to find another point. Notice on the graph the point found is (-2, -8). Then complete the graph for that portion of the function.  Notice the endpoint is a solid circle since it is included in the solution.

Now, graph -2x + 4 the same way. Use -1 to find the endpoint, f(-1) = (-2)(-1) + 4 = 6, so place (-1, 6) on the graph. Find a second point using the slope. Notice on the graph the point found is (0, 4). Then complete the graph for that portion of the function. Notice the endpoint is an open circle since it is not included in the solution.