Piecewise Defined Function Examples

The function in this example is piecewise linear because each of the three parts of the graph is a line. A function made up of 3 pieces.

Definition And Examples Of Piecewise Function Define

For example a piecewise polynomial function is a function that is a polynomial on each of its sub domains but possibly a different one on each.

Piecewise defined function examples. We can create functions that behave differently based on the input x value. The function in the example below has discontinuities at x 2 and x 2. Sometimes we come across a function that requires more than one formula in order to obtain the given output.

Every other time that weve done a piecewise function the if conditions have started with the negative x values and then become more positive as we go. It looks like this. Piecewise is actually a way of expressing the function rather than a characteristic of the function itself but with additional qualification it can describe the nature of the function.

Piecewise functions a function can be in pieces. For example in the toolkit functions we introduced the absolute value function latexfleftxrightxlatex. Some simple examples the piecewise function has a straightforward syntax.

When x is more than 2 and less than or equal to 6 it gives the line 10 x. Piecewise defined functions can also have discontinuities jumps. Piecewise functions this worksheet contains a number of examples of the use of the piecewise function.

Always read the problem carefully or youll commit a terrible math blunder. When x is less than 2 it gives x 2 when x is exactly 2 it gives 6. A solid dot means including an open dot means not including.

That doesnt have to be the case though. Every piece is specified by a boolean condition followed by an expression.

Piecewise Absolute Value And Step Functions