2-1

//Piece-Wise Functions//

**__EXAMPLE 1__**



When we are graphing piece use functions we are really graphing several functions at once, except we are only going to graph them on very specific intervals. In this case we will be graphing the following two functions.



We have to be careful with what is going on right at x = 1 since technically that will only be valid for the bottom function. For now, we will use x = 1 in both functions. The first thing to do here is to get a table of values for each function on the specific range.



Here is a sketch of the graph and notice how we denoted the points at x = 1. For the top function we used an open dot for the point at x = 1 and for the bottom function we used a closed dot at x = 1. In this way we make it clear on the graph that only the bottom function really has a point at x = 1.



Notice that since the two graphs don’t meet at x = 1 we left a blank space in the graph. Do NOT connect these two points with a line. There really does need to be a break there to signify that the two portions do not meet at x = 1. Sometimes the two portions will meet at these points and at other times they won’t. We shouldn’t ever expect them to meet or not to meet until we’ve actually sketched the graph.

**__EXAMPLE 2__**



In this case, we will be graphing three functions on the ranges given above. So, as with the previous example we will get function values for each function in its specified range and we will include the endpoints of each range in each computation. When we graph we will acknowledge which function the endpoint actually belongs with by using a closed dot as we did previously. Also, the top and bottom functions are o we don’t really need more than two points for these two. We’ll get a couple more points for the middle function.



Here is the graph:



Note that in this case two of the portions meet at the breaking point x = 1 and at the other breaking point, x = -2, they didn’t meet up.

**PRACTICE:** Given,



Evaluate each of the following:

a) 112 b) 52 c) 10 d) 10 e) -125
 * ANSWERS **:

//CW/ HW//

Print out your copy. Tomorrow 2/2 you need to scan this and email it to me at jessica.kelly@craven.k12.nc.us