Question

Definiți analitic funcția al cărei grafic este reuniunea semidreptelor reprezentate:​

Answer 1

$\it a)\\ \\ \left.\begin{aligned}\it f(0)=0\ \ \ \ \ \ \ \ \ \ \ \ \\ \\ \it f(-1)=f(1)=1\\ \\ \it f(-2)=f(2)=2\end{aligned} \right\} \Rightarrow f(x)=|x|\\ \\ \\ b)\\ \\ \left.\begin{aligned}\it f(0)=4\ \ \ \ \ \ \ \ \ \ \ \ \\ \\ \it f(-1)=f(1)=3\\ \\ \it f(-4)=f(4)=0\end{aligned} \right\} \Rightarrow f(x)=4-|x|$

$\it c)\\ \\ \left.\begin{aligned}\it f(0)=-2\ \ \ \ \ \ \ \ \ \ \ \ \\ \\ \it f(-1)=f(1)=-1\\ \\ \it f(-2)=f(2)=0\end{aligned} \right\} \Rightarrow f(x)=|x|-2$