Piecewise functions are pretty easy once you get the hang of it. Here is how I would graph one:
Start out by determining the points you want to graph.
First, look at your top function's domain. In the case of this problem, the domain is x < -4 for the function . That means we will be graphing the function of 4 + 2x for all of the values less than negative 4, not including negative 4. I usually like to come up with two or three points for each function, so in this case, Even though -4 is not included in the domain, we still want to choose -4 as one of our values. I would also pick -5 and -6.  Plug these values in for x and solve. That will get you -4, -6, and -8 respectively. Next, look at your middle function's domain, which is -4 ≤ x ≤ 5. This means that we will be graphing the function -2x for every value between -4 and 5, including 4 and five. For the table, I would use the values -4, 0, and 5. When you plug them in, you get 8, 0, and -10 respectively. Lastly, look at your last function's domain, which is x > 5 for this problem. This just means that we will be using this graph for any values greater than 5, not including the 5. For the table, I would use the values 5, 6, and 7, which will give you 10, 12, and 14 respectively. At this point, your chart should look something like this (see picture of chart)
Next, plot your points on a coordinate plane.
Two things to keep in mind: open circles DO NOT include the point, but closed circles DO. his is where the table above comes into play. We decided for the first function that -4 isn't included, but still included it in our table. That is because even the value -4.000000001 is, which is too hard to calculate exactly. You will graph an open circle at the point (-4, -4). Repeat this step with the point (5, 10), as that will be an open circle since it isn't included. The points (-4, 8) and (5, -10) will be included in the graph, since they are included in the domain, so graph them with a closed circle. The remaining points in your chart are for reference. I would plot them, but I would do it lightly so as not to get confused with the other more important points. Your final graph should look something like this (see picture of graph). Â
Hope this helps! If you have any more questions or something isn't clear in my explanation, just let me know :)
