First of all, I am using only basic parent functions and their transformations that my students are already familiar with (linear, quadratic, and absolute value). They do not need to plot points, because they already know how to sketch these graphs. I spent some time reviewing these before the lesson.
I start out with the idea of a restricted domain. Students sketch the function, using the entire coordinate plane . . .
Then we worry about this "if" that comes after the function. Students color the restricted domain, and the corresponding portion of the x-axis.
Then they draw vertical lines to enclose the restricted area and shade it in completely.
And then they erase everything that is not in the restricted area.
We practiced these for a while before moving on to piecewise.
For piecewise, we shaded each restricted domain with a different color. Then shade in the corresponding restricted areas.
By the time we reached this point, most students could draw the graphs within the restricted areas without drawing the entire graph and erasing.
I've taught this lesson before, but pairing it with colored pencils was a first for me. I am pretty happy with the results, especially considering that a bunch of them are *DONE* and have started to shut down for summer.
Secret to motivating students this time of year, anyone?
Or, to get everyone to at least bring a pencil?