Learning Resources

Investigation 7: Piecewise Functions

Step A

You should verify that the graph is indeed correct. To do so, examine each part of the piecewise function separately.

The first part contains the equation of a parabola. Identify the vertex from the equation and verify that it is indeed the vertex of the partially graphed parabola. The domain of this parabola is restricted to x 0. Determine the point (0, f(0)) and verify that it is indeed the endpoint of the graph. As well, you can use the equation, along with its restricted domain, to determine a few additional points that should be found on the graph. Then examine the graph to verify their existence. 

The second part of the function involves a linear function with a restricted domain. Identify the slope and y-intercept of the equation and check them on the graph.