Examples of solving DEs will be illustrated later. Such functions can be plotted to determine their behavior.īesides evaluating limits, you can do operations such as computing derivatives, integrating, and solving differential equations with piecewise functions. The next several Maple command lines make use of the following piecewise function:į := piecewise x ≤ − 1, − x, x ≤ 1, x 2, 1 īecause of the division by zero, points such as x = 1 cannot be substituted. Every piece is specified by a Boolean condition followed by an expression. The piecewise function has a straightforward syntax. So to find the range of a piecewise function, graph it first.This worksheet contains a number of examples of the use of the piecewise function. The range is the set of all y-values that its graph covers. The domain of a piecewise function is the union of all intervals that are given in its definition. How to Find Domain and Range of a Piecewise Function? Its graph has more than one part and yet it is possible to graph it without lifting the pencil. What is a Piecewise Continuous Function?Ī piecewise continuous function is a function that is piecewise and continuous. For example, the absolute value function, step function (floor function or greatest integer function), ceiling function, etc are examples of piecewise linear functions. Give an Example of a Piecewise Linear Function.Ī piecewise linear function is a piecewise function in which all pieces correspond to straight lines. Substitute the given input in the function from the last step.Just see which of the given intervals that input lies in.To solve the value of a piecewise function at a specific input: If the left/right endpoint is ∞ or -∞ then extend the curve on that side accordingly.Plot all the points (put open dots for the x-values that are excluded) and join them by curves.Substitute every x value in the corresponding expression of f(x) that gives value in the y-column.Include endpoints (in the column of x) of each interval in the respective table along with several other random numbers from the interval.Make a table (with two columns x and y) for each definition of the function in the respective intervals.Here is an example to understand these steps.Įxample: Graph the piecewise defined function \(f(x)=\left\\right.\). Now, just plot all the points from the table (taking care of the open dots) in a graph sheet and join them by curves.Substitute each x value from every table in the corresponding definition of the function to get the respective y values.Take 3 or more numbers for x if the piece is NOT a straight line. ![]() If the piece is a straight line, then 2 values for x are sufficient. In each table, take more numbers (random numbers) in the column of x that lie in the corresponding interval to get the perfect shape of the graph. ![]() If the endpoint is excluded from the interval then note that we get an open dot corresponding to that point in the graph. Include the endpoints of the interval without fail.
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