Step 3: While you are in the “y1 =” slot, press CATALOG and then press the period “.” (for “W”, which is above the period key). Clear any equations in the y=editor by using the arrow keys and pressing the CLEAR key. Step 2: Press the diamond key and then press F1 to enter the y=editor. f(x) = x + 5, x is less than or equal to 0.Sample problem: graph the following piecewise functions: Piecewise Functions TI 89 “when”: Example While plotting (and differentiating) piecewise functions by hand can become problematic-especially if you have three or more equations to deal with-the TI89 makes graphing piecewise functions a snap with its “when(“ command. In other words, instead of one equation to input, you may have several making up one large function. Piecewise functions are functions that are in separate pieces. Piecewise Functions TI 89 “when(” Command You now have a neat graph of the piecewise function. Finally, erase your light pencil drawing.Look again at your intervals, and darken/color the graph of your functions only in the relevant intervals: between the vertical lines which mark the changes.The first two steps to drawing a piecewise function. You will have two or more functions which may cross don’t worry about that. In our case, we would be drawing just one line, at x= -3. 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. Piecewise SmoothĪ piecewise continuous function is piecewise smooth if the derivative is piecewise continuous. But as long as it meets all of the other requirements (for example, as long as the graph is continuous between the undefined points), it’s still considered piecewise continuous. A function could be missing, say, a point at x = 0. Perhaps surprisingly, nothing in the definition states that every point has to be defined. The limit doesn’t exist on one side at x = 0, because of the vertical asymptote.

If a function has a vertical asymptote like this, even at the end of an interval, then it isn’t piecewise continuous.Īn example of a non-piecewise continuous function: 1/x. 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. A piecewise function is a function made up of different parts.

Piecewise defined function calculator