The Piecewise Function $f(x)$ Has Opposite Expressions. $f(x)=\left\{\begin{array}{ll} 2 X-1, & X<0 \\ 0, & X=0 \\ -2 X+1, & X>0 \end{array}\right.$ Which Is The Graph Of $f(x)$?

Piecewise functions can be defined using the common functional notation, where the body of the function is an array of functions and associated subdomains. Piecewise functions let us make functions that do anything we want! Jul 23, 2025a piecewise function is a function that is defined differently over different intervals of its domain.

Instead of using a single equation for all inputs, it assigns distinct expressions to specific. Piecewise functions follow differnt rules depending on the value of x. Learn how to solve, graph, and read piecewise functions here!

Piecewise functions piecewise functions are functions that have multiple pieces, or sections. They are defined piece by piece, with various functions defining each interval. A piecewise function is a function in which more than one formula is used to define the output.

Each formula has its own domain, and the domain of the function is the union of all these smaller domains. Piecewise functions are strongly tied to domain and range. The pieces are defined using functions or relations along with a specified domain (or sometimes range, like a vertical line).

This definition of the function v is called a “piecewise definition.” because each of the pieces in this definition is constant, the function v is called a piecewise constant function. Graphing a piecewise function can be accomplished by simply graphing the functions found in the respective "pieces", limiting the points drawn for each piece to the x -values that satisfy the. Let’s draw these piecewise functions and determine if they are continuous or non-continuous.

Note how we draw each function as if it were the only one, and then “erase” the parts that aren’t needed.