# 微积分网课代修|预备微积分代写precalculus辅导|MATH113 Graphing Piecewise-Defined Functions

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## 微积分网课代修|预备微积分代写precalculus辅导|Graphing Piecewise-Defined Functions

Sometimes, we come across a function that requires more than one formula in order to obtain the given output. For example, in the toolkit functions, we introduced the absolute value function $f(x)=|x|$. With a domain of all real numbers and a range of values greater than or equal to 0 , absolute value can be defined as the magnitude, or modulus, of a real number value regardless of sign. It is the distance from 0 on the number line. All of these definitions require the output to be greater than or equal to 0 .
If we input 0 , or a positive value, the output is the same as the input.
$$f(x)=x \text { if } x \geq 0$$
If we input a negative value, the output is the opposite of the input.
$$f(x)=-x \text { if } x<0$$
Because this requires two different processes or pieces, the absolute value function is an example of a piecewise function. A piecewise function is a function in which more than one formula is used to define the output over different pieces of the domain.

## 微积分网课代修|预备微积分代写precalculus辅导|piecewise function

$f(x)=\left{\begin{array}{lll}\text { formula } 1 & \text { if } x \text { is in domain } 1 \text { formula } 2 & \text { if } x \text { is in domain } 2 \text { formula } 3 \text { if } x \text { is in domain } 3\end{array}\right.$

$\$ \$$|x|=\mid l e f t{ x if x \geq 0-x \quad if x<0 右。 \ \$$