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.
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. Make a table with two columns labeled x and y corresponding to each interval.Write the intervals that are shown in the definition of the function along with their definitions.For example, f(x) = ax + b represents a linear function (which gives a line), f(x) = ax 2 + bx + c represents a quadratic function (which gives a parabola), etc, so that we will have an idea of what shape the piece of the function would result in. First, understand what each definition of the function represents.Here are the steps to graph a piecewise function.
We already know that the graph of a piecewise function has multiple pieces where each piece corresponds to its definition over an interval.
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