Quandaries
and Queries 

Hi, my name is Dani. I'm in tenth grade Algebra 2, and I'm learning about a lot of different kinds of functions, and I can't quite seem to understand how every part of the piecewise function works. I understand most of it, I think, but I've been looking at an example in my math book, and I'm not sure how they got the answer they did. The part I don't understand reads: "Graph f(x) = x4 if x<2" and "Identify the domain and range." The picture in the book shows an open circle at (2,2), with an arrow going down and to the left with the slope being one. How did they get the open circle to be at (2,2), and why does the arrow point where it does? Thanks! 

Hi Dani, I think the diagram you are describing is
When I look at this problem and the expression is y = x  4 I see the line with slope 1 and through the point (0,4), that is I see
But the function described in the problem is only defined for x < 2 so I should erase the part of the line that has xxalues larger than or equal to 2.
But from this diagram alone I can't tell if the function is defined at x=2 or not. There might be a point (2,4) on the graph, I can't tell. To show that the function is not defined at 2 one technique is to put a small open circle at the "missing point", (2,4). Penny 

