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Chapter 2: Problem 104

What is a piecewise function?

Short Answer

Expert verified
A piecewise function is a function defined by different formulas for different parts of its domain. The formula used depends on the input value. An example is the absolute value function.

Step by step solution

01

Definition

A piecewise function is a function that is defined by several different formulas or 'pieces', each applying to a different section of its domain.
02

Operation

The specific formula used to calculate a piecewise function's value depends on the value of its input. The domain of the function is divided into sections, and a different formula is used for each section. The formulas are usually chosen so that the function is continuous, meaning that it doesn't have any abrupt changes or jumps.
03

Example

A simple example of a piecewise function is the absolute value function. This function is defined by two different formulas: For \( x \) greater than or equal to 0, the function is equal to \( x \); and for \( x \) less than 0, the function is equal to -\( x \). So, the absolute value function can be written as: \( f(x) = \begin{cases} x & \text{if } x\geq 0\\ -x & \text{if } x < 0 \end{cases} \).

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