En funksjon kan være gitt ved forskjellige uttrykk for forskjellige $x$-verdier:
f(x) = \left\{ \begin{array}{ll}
u(x), & \textcolor{blue}{x < a} \\
v(x), & \textcolor{red}{x \ge a}
\end{array}\right.$u(x)$ gjelder når $\textcolor{blue}{x<a}$ og $v(x)$ gjelder når $\textcolor{red}{x \ge a}$.
+ Eksempel 1
f(x) = \left\{ \begin{array}{ll}
2, & \textcolor{blue}{x < 1} \\
x, & \textcolor{red}{x \ge 1}
\end{array}\right.Eksempler på funksjonsverdier:
\begin{aligned}
f(\textcolor{blue}{-1}) = 2 & \qquad \textnormal{gir punktet} (-1,2) \\
f(\textcolor{blue}{0.99}) = 2 & \qquad \textnormal{gir punktet} (0.99,2) \\
f(\textcolor{red}{1}) = 1 & \qquad \textnormal{gir punktet} (1,1) \\
f(\textcolor{red}{2}) = 2 & \qquad \textnormal{gir punktet} (2,2) \\
\end{aligned}+ Eksempel: Absoluttverdi
Absoluttverdi:
f(x) = \left\{ \begin{array}{ll}
-x, & \textcolor{blue}{x < 0} \\
x, & \textcolor{red}{x \ge 0}
\end{array}\right.Eksempler på funksjonsverdier:
\begin{aligned}
f(\textcolor{blue}{-1}) = 1 & \qquad \textnormal{gir punktet} (-1,1) \\
f(\textcolor{blue}{-0.01}) = 0.01 & \qquad \textnormal{gir punktet} (-0.01,0.01) \\
f(\textcolor{red}{0}) = 0 & \qquad \textnormal{gir punktet} (0,0) \\
f(\textcolor{red}{2}) = 2 & \qquad \textnormal{gir punktet} (2,2) \\
\end{aligned}+ Eksempel: Heavisides step funksjon
f(x) = \left\{ \begin{array}{ll}
0, & \textcolor{blue}{x < 0} \\
1, & \textcolor{red}{x \ge 0}
\end{array}\right.Eksempler på funksjonsverdier:
\begin{aligned}
f(\textcolor{blue}{-1}) = 0 & \qquad \textnormal{gir punktet} (-1,0) \\
f(\textcolor{blue}{-0.01}) = 0 & \qquad \textnormal{gir punktet} (-0.01,0) \\
f(\textcolor{red}{0}) = 0 & \qquad \textnormal{gir punktet} (0,0) \\
f(\textcolor{red}{2}) = 1 & \qquad \textnormal{gir punktet} (2,1) \\
\end{aligned}+ Eksempel: Diracs impulsfunksjon
f(x) = \left\{ \begin{array}{ll}
0, & \textcolor{blue}{x < 0} \\
\infty, & \textcolor{green}{x = 0} \\
0, & \textcolor{red}{x > 0}
\end{array}\right.Eksempler på funksjonsverdier:
\begin{aligned}
f(\textcolor{blue}{-1}) = 0 & \qquad \textnormal{gir punktet} (-1,0) \\
f(\textcolor{blue}{-0.01}) = 0 & \qquad \textnormal{gir punktet} (-0.01,0) \\
f(\textcolor{green}{0}) = \infty & \qquad \textnormal{gir ikke noe punkt (hvor plottes uendelig?)} \\
f(\textcolor{red}{0.01}) = 0 & \qquad \textnormal{gir punktet} (0.01,0) \\
f(\textcolor{red}{2}) = 0 & \qquad \textnormal{gir punktet} (2,0) \\
\end{aligned}