![]() Even though there looks like a gap from $y=1$ to $y=2$, the piece of the function $f(x)=x^2$ includes those values. The range begins at the lowest $y$-value, $y=0$ and is continuous through positive infinity. Graphing Piecewise Functions Example 1: Consider the piecewise definition of the absolute value function: We use piecewise functions to describe situations in which a rule or relationship changes as the input value crosses certain “boundaries.” Piecewise functions are defined using the common functional notation, where the body of the function is an array of functions and associated intervals. Is a function in which more than one formula is used to define the output over different pieces of the domain. A closed circle means the end point is included.Ī domain that is part of a larger domain.įor a real number, its numerical value without regard to its sign formally, $-1$ times the number if the number is negative, and the number unmodified if it is zero or positive.Ī function in which more than one formula is used to define the output over different pieces of the domain. strictly less than or strictly greater than. ![]() An open circle at the end of an interval means that the end point is not included in the interval, i.e.A horizontal gap means that the function is not defined for those inputs. Piecewise functions may have horizontal or vertical gaps (or both) in their functions.For a real number, its value is $-x$ when $x<0$ and its value is $x$ when $x\geq0$. The absolute value, $\left | x \right |$ is a very common piecewise function. ![]()
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