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On your graph paper, draw vertical dotted lines at each of the values of x listed.To graph an piecewise function, first look at the inequalities. This is usually easier to see if you graph the function. The actual value will be given by 16 – 2x, so: At x = 0, x > – 3, so it is the second part of the piecewise function that applies to your situation. If you try to evaluate it by calculating 2x + 14 = 14 (the first piece), you would be wrong. The first thing to note is that this particular function has two pieces, split at x = -3. For example, suppose you wanted to evaluate the following function at x = 0. Evaluating a Piecewise Functionįirst identify which piece of your function it belongs in. However, the function is not continuous at the integers, so it isn’t an example of this type of function. For example, the square wave function is piecewise, and it certainly looks like a piecewise continuous function. Just because a graph looks like it’s a piecewise continuous function, it doesn’t mean that it is. If a function has a vertical asymptote like this, even at the end of an interval, then it isn’t piecewise continuous.Ī piecewise continuous function is piecewise smooth if the derivative is piecewise continuous. As an example, the function sin(1/x) is not piecewise continuous because the one-sided limit f(0+) doesn’t exist. When trying to figure out if a function is piecewise continuous or not, sometimes it’s easier to spot when a function doesn’t meet the strict definition (rather than trying to prove that it is!).Īn important part of this definition is that the one-sided limits have to exist. In addition, both of the following limits exist and are finite (Doshi, 1998):Įxamples of a Function that is Not Piecewise Continuous In other words, the function is made up of a finite number of continuous pieces.Ī piecewise continuous function f(x), defined on the interval (a < x < b), is continuous at any point x in that interval, except that it could be discontinuous for some finite points x i (i = 1, 2, 3…) such that a < x i < b. Piecewise Continuous FunctionĪ piecewise continuous function is continuous except for a certain number of points. It may or may not be a continuous function. More specifically, it’s a function defined over two or more intervals rather than with one simple equation over the domain. Your drawing should look like Figure 1.A piecewise function is a function made up of different parts. To graph the second function, y = x 2 from with domain (1,∞), type function and then press the ENTER key. The ∞ symbol can is located on the drop-down list box located to the immediate right of the input box.ģ. So to graph y = 1 – x with domain (-∞,1] type function and the press the ENTER key.
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The syntax of the function command is function, where f is the equation of the function, a is the start x-value and b is the end x-value. In graphing a piecewise function, we will use the function command of GeoGebra. If not, from the menu bar, click View>Axes to display it in the GeoGebra window.Ģ. In this tutorial, we will not need the coordinate Axes so be sure that it is displayed. The output applet of this tutorial can be viewed here.ġ. If you want to follow this tutorial step-by-step, you can open the GeoGebra window in your browser by clicking here. Click the image to go to view the applet.